content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Power series expansion
January 8th 2009, 02:09 AM #1
Member
Joined
Oct 2008
From
Melbourne
Posts
166
"By adapting the power series expansion (centred on c = 0) of $h(t) = \frac{1}{1-t}$ , write down a power series expansion (with the indicated centre) for each of the following functions, and
indic... | 5 | [
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0.00811767578125,
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0.0023956298828125,
-0.0286865234375,
0.011962890625,
0.0174560546... | 25,400 | 25400 | |
Proof by induction
May 15th 2013, 11:29 PM #1
Newbie
Joined
May 2013
From
morroco
Posts
14
Thanks
1
Proof by induction
Hello guys could anyone help find a solution to this problem,
Show that:
3 x 5^(2n-1) + 2^(3n-2) is divisble by 17 (for every n on N*)
This is what i did :
ver... | 4 | [
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-0.02087... | 25,401 | 25401 | |
help bivariate
March 22nd 2008, 03:42 AM
gracey
help bivariate
Five observations of bivariate data produce the following results, denoted as (xi, yi)for i =1, 2, 3, 4, 5.
(13, 2.7) (13, 4.0) (18, 2.8) (23, 3.3) (23, 2.2)
[Σ x = 90, Σ y = 15.0, Σ x2 = 1720, Σ y2 = 46.86, Σ xy = 264.0.]
The regressi... | 4 | [
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-0.0... | 25,402 | 25402 | |
4 Manifolds all of whose geodesics are lines
Next: 5 Conclusion Up: Axiomatic and Coordinate Geometry Previous: 3 Riemannian Geometry
In order to tie up the first two sections we need to have a notion analogous to lines in a general Riemannian manifold--this is provided by geodesics or energy minimising paths.
T... | 4 | [
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problem with sequence and means
June 24th 2012, 02:16 AM #1
Member
Joined
Jun 2010
From
Zewail University - Cairo - Egypt
Posts
136
problem with sequence and means
the A.S mean of two no.s : 8,2x^2 exceeds their positive G.M by 9 .Find X
i got it 5, -5 is that right?
Re: problem with sequence an... | 4 | [
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Solving log/exponential problem
February 17th 2011, 03:59 PM #1
Newbie
Joined
Feb 2011
Posts
15
Solving log/exponential problem
So I have a question about this problem:
5e^2-x = 7e^x
i know you need to apply Ln to both sides, but first can you bring the 5 up to the exponent? or does this not ap... | 4 | [
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0.04... | 25,405 | 25405 | |
Proof that Upper Riemann Integral > Lower Riemann Integral...?
August 3rd 2007, 04:00 PM #1
Junior Member
Joined
Aug 2007
Posts
45
heyyy guys....
im new at this level of maths so i would appreciate a lil bit of help here and there
i want to show that
lower riemann integral $\int^b_a f(x)dx \l... | 4 | [
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... | 25,406 | 25406 | |
the encyclopedic entry of Continuously Compounded Real Return
Nominal return
Let
p[t]
be the price of a security at time
t
, including any cash dividends or
interest
, and let
p[t − 1]
be its price at
t
− 1. Let
RS[t]
be the simple return on the security from
t
− 1 to
t
,
$1 + RS_\left\{t\right\}=... | 4 | [
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Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System
Journal of Control Science and Engineering
Volume 2013 (2013), Article ID 763165, 19 pages
http://dx.doi.org/10.1155/2013/763165
Research Article
Model Reduction Using Proper Orthogonal Decomposition and Predict... | 4 | [
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Geometric series and such..
February 21st 2007, 05:10 PM #1
Member
Joined
Nov 2006
From
chicago
Posts
156
Geometric series and such..
The sum of an infinite geometric series is 36. The second term of the series is 8. Find two possibilities for combinations of a (the first term) and r (the common rati... | 4 | [
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A question out of curiosity....
April 11th 2012, 01:16 PM #1
Newbie
Joined
Apr 2012
From
London
Posts
3
Thanks
1
A question out of curiosity....
Can a number have 2 square roots? If you say no, surely 4 has 2 squared and minus 2 squared bothe as square roots? Do minus numbers get involved in squa... | 5 | [
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Joint PDF
May 6th 2009, 04:35 AM
panda*
Joint PDF
The joint probability distribution is given by,
$f_{(X,Y)}(x,y) = 2$ if $0 \leq x \leq y \leq 1$, 0 otherwise.
(i) Determine the marginal density functions of X and Y. Check that it is indeed a pdf.
(ii) Calculate the means $\mathbb{E}X$ and VarX.
... | 4 | [
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Math Help
April 7th 2006, 06:24 AM #1
Newbie
Joined
Apr 2006
Posts
3
integration
hi, is there any method of integrating a hyperbolic or trignometric function whos degree is 4, such as (tanx)^4, (cosechx)^4 WITHOUT resorting to reduction formulae??
Sure, there just isn't a "golden recipe" which will... | 5 | [
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0.0252685546875... | 25,412 | 25412 | |
Lecture 16: Continuation: More General Periods
Okay, that's, so to speak, the text for today. The Fourier series, and the Fourier expansion for f(t), so f of t, if it looks like this should be periodic, and two pi should be a period. Sometimes
people rather sloppily say periodic with period two pi, but that's a little ... | 5 | [
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... | 25,413 | 25413 | |
Polynomials and rational functions
July 12th 2010, 03:25 AM
Glitch
Polynomials and rational functions
The question asks "State whether the function is a polynomial, a rational function (but not a polynomial), or neither."
This is the function:
$F(x) = \frac{x^3 - 3x^{3/2} + 2x}{x^2 - 1}$
It looks ... | 4 | [
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A Stochastic Two Species Competition Model: Nonequilibrium Fluctuation and Stability
International Journal of Stochastic Analysis
Volume 2011 (2011), Article ID 489386, 7 pages
http://dx.doi.org/10.1155/2011/489386
Research Article
A Stochastic Two Species Competition Model: Nonequilibrium Fluctuation and Stability
... | 4 | [
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0.0200195... | 25,415 | 25415 | |
Norm of an Operator
April 19th 2010, 02:12 PM
ejgmath
Norm of an Operator
I need to show that the operator $T:L^2([0,1],\mathbb{R}) \rightarrow L^2([0,1],\mathbb{R})$ defined by $(Tf)(x)=xf(x)$ has norm 1
There is a hint on the question saying show it must be at least $1-\frac{1}{n}$ for all $n$
The no... | 5 | [
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Solving system of ODE's
November 29th 2009, 04:45 PM #1
Newbie
Joined
Nov 2009
Posts
19
Solving system of ODE's
I have a 2 seperate systems i am trying to solve but don't seem to know any technique that will solve this problem (the other is similar in nature to this one)
Problem:
$\frac{dC_{0}}... | 5 | [
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eccentricity application
May 23rd 2009, 11:40 PM #1
Junior Member
Joined
Feb 2009
Posts
34
eccentricity application
can someone help me with this problem ( I'm quite new with some terms)
A satellite is to be placed in an elliptical orbit, with the center of the earth as one focus. The satellite's ma... | 4 | [
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Optimization of GMAW Process Parameters Using Particle Swarm Optimization
ISRN Metallurgy
Volume 2013 (2013), Article ID 460651, 10 pages
http://dx.doi.org/10.1155/2013/460651
Research Article
Optimization of GMAW Process Parameters Using Particle Swarm Optimization
^1Department of Mechanical Engineering, Valia Koon... | 4 | [
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0.090332031... | 25,419 | 25419 | |
Linear Matrix Inequalities in Multirate Control over Networks
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 768212, 22 pages
http://dx.doi.org/10.1155/2012/768212
Research Article
Linear Matrix Inequalities in Multirate Control over Networks
Departamento de Ingeniería de Sistemas y Automática, ... | 4 | [
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-0.06298... | 25,420 | 25420 | |
Help me in derivation of limit
in limits for 1^∞ type of indeterminate form, the direct solution is e^{g(x)[f(x)-1]}
I am not sure what you mean by "direct solution" but you can convert the form so L'hosiptials rule can be used. If $\lim_{x \to \infty} f(x)=1$ and $\lim_{x \to \infty} g(x)=\infty$ then $[f(x)]^{g
(x)}... | 5 | [
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-0.046630859375,
-0.02... | 25,421 | 25421 | |
when is this true for integral
what is the condition for this statement to be true?
Use the definition of the derivative. $f'(x)=\lim_{h \to 0}\frac{\sqrt{x+h}-\sqrt{x}}{h}$ Multilpy the numerator and denominator by the conjugate to get $f'(x)=\lim_{h \to 0}\frac{\sqrt{x+h}-\sqrt
{x}}{h}\left( \frac{\sqrt{x+h}+\sqrt{x... | 5 | [
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0.0208740234375,
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Proposition 2
If, when the less of two unequal magnitudes is continually subtracted in turn from the greater that which is left never measures the one before it, then the two magnitudes are incommensurable.
There being two unequal magnitudes AB and CD, with AB being the less, when the less is continually subtracted i... | 4 | [
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... | 25,423 | 25423 | |
Modeling and Control for Giant Magnetostrictive Actuators with Rate-Dependent Hysteresis
Journal of Applied Mathematics
Volume 2013 (2013), Article ID 427213, 8 pages
http://dx.doi.org/10.1155/2013/427213
Research Article
Modeling and Control for Giant Magnetostrictive Actuators with Rate-Dependent Hysteresis
School... | 4 | [
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Strong Pullback Attractors for Nonautonomous Suspension Bridge Equations
ISRN Applied Mathematics
Volume 2014 (2014), Article ID 253532, 8 pages
http://dx.doi.org/10.1155/2014/253532
Research Article
Strong Pullback Attractors for Nonautonomous Suspension Bridge Equations
College of Mathematics and Statistics, North... | 4 | [
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... | 25,425 | 25425 | |
Soliton Solutions for the Wick-Type
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 327682, 9 pages
http://dx.doi.org/10.1155/2012/327682
Research Article
Soliton Solutions for the Wick-Type Stochastic KP Equation
^1Department of Information and Computation of Science, Guangxi University of Technology,... | 5 | [
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-0.0... | 25,426 | 25426 | |
u-sub integration help
April 29th 2009, 03:13 PM #1
Newbie
Joined
Apr 2009
Posts
1
u-sub integration help
guys first timer here. cant quite figure this one out.
ʃ dt/ t√(5tē-3)
it looks to me to be a sec^-1u type of question but i cant seem to find the correct u value. any help from you smar... | 5 | [
-0.043212890625,
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-0.02734375,
-0.0289306640625,
-0.08544921875,
-0.0517578125,
0.000789642333984375,
-0.00408935546875,
-0.0157470703125,
0.036376953125,
-0.00848388671875,
0.0164794921875,
0.0245361328125,
-0.087890625,
-0.01348876953125,
0.03515625,
... | 25,427 | 25427 | |
Need some help ! newbie here !
January 11th 2013, 05:55 PM #1
Need some help ! newbie here !
hi i'm Jhaycian Velasquez 19 years of age an engineering student
can u please help me out of this give me some figure
two observers who are 2 miles apart on a horizontal plane observe a balloon in a same vertica... | 4 | [
-0.003021240234375,
0.12158203125,
-0.013916015625,
-0.016357421875,
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0.040771484375,
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-0.08349... | 25,428 | 25428 | |
Simple Interest Challenge Problem
October 7th 2012, 01:58 PM #1
Newbie
Joined
Oct 2012
From
Alberta Canada
Posts
6
Simple Interest Challenge Problem
A father wanted to show his son what it might be like to borrow money from a financial insitution. When his son asked if he could borrow $120 the father... | 4 | [
0.026123046875,
0.08154296875,
-0.044677734375,
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0.002899169921875,
0.051025390625,
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0.10693359375,
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0.0361328125,
-0.01251220703125,
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0.0269775390625,
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Compact, bounded, closed-range operators on Hilbert spaces have finite rank
May 26th 2012, 12:54 AM
UniversityMathsStudent
Compact, bounded, closed-range operators on Hilbert spaces have finite rank
Hi,
I am trying to prove that if $T:H\to{H}$ is a compact, bounded operator with closed range, where $H$ is a... | 5 | [
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... | 25,430 | 25430 | |
STATS_MW_TEST
Description of the illustration stats_mw_test.gif
A Mann Whitney test compares two independent samples to test the null hypothesis that two populations have the same distribution function against the alternative hypothesis that the two distribution
functions are different.
The STATS_MW_TEST does not as... | 5 | [
-0.010009765625,
0.0115966796875,
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Factorisation
what about $(x^3+i)(x^3-i)$ expanding back out to check $x^6+x^3i-x^3i-i^2$ $x^6-i^2$ $x^6-(-1)$ $x^6+1$
If you're factorising over the Real Numbers, it does not factorise. If you're factorising over the Complex Numbers, change it to a difference of two squares. $x^6 + 1 = (x^3)^2 - i^2$ $= (x^3 + i)(x^
... | 5 | [
-0.0250244140625,
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0.0976562... | 25,432 | 25432 | |
[SOLVED] Functions
March 22nd 2009, 08:53 AM #1
Member
Joined
Jan 2009
From
earth
Posts
167
Given $f(x)= x^2 -2x +7$ and $g(x)= 2x-3$
find a. $(f+g)(2)$
b. $(f.g)(2)$
c. $(f/g)(2)$
d. $(f.g)(x)$
Thanks in advance. I don't even know where to start
$(f+g)(2)=f(2)+g(2)$
... | 4 | [
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0.116210... | 25,433 | 25433 | |
An Alternative Method for the Study of Impulsive Differential Equations of Fractional Orders in a Banach Space
International Journal of Differential Equations
Volume 2013 (2013), Article ID 191060, 12 pages
http://dx.doi.org/10.1155/2013/191060
Research Article
An Alternative Method for the Study of Impulsive Differe... | 5 | [
-0.10693359375,
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0.0225830078125,
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-0.044189453125,
-... | 25,434 | 25434 | |
-Adic Hardy Operators and Their Commutators on
Journal of Function Spaces and Applications
Volume 2013 (2013), Article ID 359193, 10 pages
http://dx.doi.org/10.1155/2013/359193
Research Article
Boundedness of -Adic Hardy Operators and Their Commutators on -Adic Central Morrey and BMO Spaces
Department of Mathematic... | 5 | [
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... | 25,435 | 25435 | |
Dice Calculation for Tabletop RPG
July 26th 2010, 01:17 PM #1
Newbie
Joined
Jul 2010
Posts
2
Dice Calculation for Tabletop RPG
Thanks for your time.
I believe this would fit under the Calculus heading since it appears to be related to finding the maxima of a nonlinear function, though I'm not sure. ... | 4 | [
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0.0498046875,
... | 25,436 | 25436 | |
Integration by parts
February 7th 2010, 06:17 AM #1
Newbie
Joined
Feb 2010
Posts
22
Integration by parts
Integrate (x^3 dx) / square root of (1-x^2)
i have to integrate it by parts. i already tried it but my answer waa 0=0 is that possible?
how?
let u = x^3
du = 3x^2 dx0
dv = dx / sq r... | 5 | [
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0.... | 25,437 | 25437 | |
Math Help
April 30th 2009, 06:48 AM #1
Newbie
Joined
Apr 2009
Posts
8
Matrices
The matrix ( 1 2) maps Q(1,2) to R(5,7).
(1 3)
Find the 2 x 2 matrix which maps R back to Q.
Help please.
I will guess that you meant to say the following:
Code:
The matrix [ 1 2 ]
... | 5 | [
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0... | 25,438 | 25438 | |
Few pratice problems that I'm having trouble with.
March 25th 2007, 02:21 PM #1
Newbie
Joined
Mar 2007
Posts
6
Few pratice problems that I'm having trouble with.
A lighthouse is located 3km away from the nearest point P on a straight shoreline and its light makes four revolutions per minute. How fast is ... | 5 | [
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... | 25,439 | 25439 | |
containing all sub-array combinations of
Minimal arrays containing all sub-array combinations of symbols: De Bruijn sequences and tori
For
n
symbols in
m
groups, what are the smallest arrays that contain all combinations of adjacent elements?
This is a
symbolic combinatorics
question. It shares some characteris... | 5 | [
0.06787109375,
0.0189208984375,
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0.138671875,
0.00842285156... | 25,440 | 25440 | |
The Matrix Linear Unilateral and Bilateral Equations with Two Variables over Commutative Rings
ISRN Algebra
Volume 2012 (2012), Article ID 205478, 14 pages
http://dx.doi.org/10.5402/2012/205478
Research Article
The Matrix Linear Unilateral and Bilateral Equations with Two Variables over Commutative Rings
Pidstryhach... | 5 | [
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0.06... | 25,441 | 25441 | |
Practice Math Kangaroo Problems 11 to 15, Level 0304
Problem Kangur_2002_0304_11 (4 pts) http://www.mathkangaroo.org
This picture below is a sketch of a castle. Which of the lines below does not belong to the sketch?
A)
B)
C)
D)
E)
Solution: Answer: C. This is a somewhat tricky image/shape recognition problem in wh... | 4 | [
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0.072... | 25,442 | 25442 | |
Generalized Mittag-Leffler Function Associated with Weyl Fractional Calculus Operators
Journal of Mathematics
Volume 2013 (2013), Article ID 821762, 5 pages
http://dx.doi.org/10.1155/2013/821762
Research Article
Generalized Mittag-Leffler Function Associated with Weyl Fractional Calculus Operators
^1Department of Ma... | 5 | [
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Worksheet on Co-ordinate Triangle |Area of a Triangle|Formula|Polar Co-ordinates
Worksheet on Co-ordinate Triangle
In the worksheet on co-ordinate triangle we need to find the area of a triangle where the three co-ordinates of the vertices are given.
Let us recall the formula for finding the area of a triangle fo... | 4 | [
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-Norm Algorithm for MRI Phase Unwrapping
Computational and Mathematical Methods in Medicine
Volume 2014 (2014), Article ID 134058, 11 pages
http://dx.doi.org/10.1155/2014/134058
Research Article
Sparse-Representation-Based Direct Minimum -Norm Algorithm for MRI Phase Unwrapping
^1Department of Biomedical Engineering... | 4 | [
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An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 697474, 7 pages
http://dx.doi.org/10.1155/2013/697474
Research Article
An Approximate Quasi-Newton Bundle-Type Method for Nonsmooth Optimization
^1School of Mathematics, Liaoning Nor... | 4 | [
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-... | 25,446 | 25446 | |
Trig Identity?
December 13th 2010, 06:31 PM #1
Newbie
Joined
May 2010
Posts
9
Trig Identity?
I recently read somewhere that $sin(\theta)=\frac{y}{\sqrt{y^2+x^2}}$, but I cannot seem to find this identity anywhere on the internet. Does anyone know what this is called, or where I can find
the same iden... | 4 | [
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0... | 25,447 | 25447 | |
Torque question
May 4th 2010, 09:03 AM #1
Super Member
Joined
Nov 2008
Posts
597
Torque question
I just started torque so excuse me for asking a stupid question but I'm stuck trying to do the following question:
"A wheel starts from rest and rotates through 150 rad in 5 s. The net torque due to the ... | 5 | [
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0.025756... | 25,448 | 25448 | |
Proposition 14
In equal and equiangular parallelograms the sides about the equal angles are reciprocally proportional; and equiangular parallelograms in which the sides about the equal angles are reciprocally
proportional are equal.
Let AB and BC be equal and equiangular parallelograms having the angles at B equal, a... | 4 | [
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-0.0698242... | 25,449 | 25449 | |
Summation proof
February 10th 2010, 10:58 AM #1
Newbie
Joined
Feb 2010
Posts
3
Summation proof
Prove that $n*\sum_{i=0}^nx_i^2 \geq (\sum_{i=0}^nx_i)^2$
I tried proving it directly using summation identities. I then tired using induction, but I kept getting stuck.
A proof similar to this may be... | 5 | [
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the encyclopedic entry of quantum electrodynamics
Quantum electrodynamics
(
QED
) is a
relativistic quantum field theory
of
electrodynamics
. QED was developed by a number of physicists, beginning in the late 1920s. It basically describes how light and matter interact. More specifically it deals with the interac... | 4 | [
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0.034423828125,
-0.037597656... | 25,451 | 25451 | |
integration with factorials
January 14th 2009, 04:43 PM #1
Member
Joined
Jan 2009
Posts
91
integration with factorials
im having a lot of trouble showing that the
definite integral from 0 to 1 (ln x)^n dx = n!(-1)^n
if someone could help get me started cause i have no idea how to get the factori... | 5 | [
-0.01129150390625,
-0.0478515625,
0.0281982421875,
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0.03466796875,
... | 25,452 | 25452 | |
Maximum possible volume
June 6th 2011, 08:29 AM #1
Super Member
Joined
Dec 2009
Posts
755
Maximum possible volume
A circular hollow cone of height h and semi-vertical angle $30^o$ stands on a horizontal table. An upright cylinder of radius $r$ cm and height $d$ cm just fits into the cone as shown in ... | 5 | [
0.01190185546875,
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0... | 25,453 | 25453 | |
integration partial fractions
integral of (u+4)/((u^2)+4) du How would I solve for this?
THere is no need for partial fractions here $\int\frac{u+4}{u^2+4}du=\int\frac{u}{u^2+4}du+4\in t\frac{du}{u^2+4}=\frac{1}{2}\ln|u^2+4|+2\arctan\b igg(\frac{u}{2}\bigg)+C$ Also, conider the fact that
if you wanted to do this by pa... | 5 | [
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... | 25,454 | 25454 | |
Help Please! : Newton's Method
August 13th 2009, 06:59 PM #1
Help Please! : Newton's Method
Hi! We're doing Newton's method and I'm SO LOST! Lecturer only gave one example. Can anyone help me with the following question so I can compare? Don't know where to start! Annotations through
your workings would be gr... | 4 | [
-0.08203125,
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0.0235595703125,
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-0.033691406... | 25,455 | 25455 | |
Predicates Help
March 4th 2009, 09:31 AM
M.A.T.H
Predicates Help
We have the predicates E and O describing integers, defined by E(n) is true if n is even, and O(n) is true if n is odd.
(a) Express in predicate calculus notation the sentence the sum of two odd integers is even.
Can any please pleas... | 4 | [
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the encyclopedic entry of Percolation_theory
In
mathematics
,
percolation theory
describes the behavior of
connected
clusters in a
random graph
. The applications of percolation theory to
materials science
and other domains are discussed in the article
percolation
.
Introduction
A representative question ... | 4 | [
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0.0400390625,
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0.044921875,
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0.004302978515625,
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Null Steering in Failed Antenna Arrays
Applied Computational Intelligence and Soft Computing
Volume 2011 (2011), Article ID 692197, 9 pages
http://dx.doi.org/10.1155/2011/692197
Research Article
Null Steering in Failed Antenna Arrays
Department of Electronics and Computer Engineering, Indian Institute of Technology ... | 4 | [
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0.05224609375,
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-0.... | 25,458 | 25458 | |
Fuzzy Retractions of Fuzzy Open Flat Robertson-Walker Space
Advances in Fuzzy Systems
Volume 2013 (2013), Article ID 342805, 7 pages
http://dx.doi.org/10.1155/2013/342805
Research Article
Fuzzy Retractions of Fuzzy Open Flat Robertson-Walker Space
^1Mathematics Department, Faculty of Science, Taibah University, Madi... | 5 | [
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-0.0781... | 25,459 | 25459 | |
Continuity with product of the range
April 4th 2009, 08:40 AM #1
Junior Member
Joined
Feb 2008
Posts
63
Continuity with product of the range
Let $f_1: X \rightarrow Y_1$ and $f_2: X \rightarrow Y_2$ be continuous functions. Show that $h: X \rightarrow Y_1\times Y_2$ defined by $h(x)=(f_1(x),f_2(x))$, is ... | 5 | [
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0.0026397705078125,
-0.020385742187... | 25,460 | 25460 | |
Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Applications
Abstract and Applied Analysis
Volume 2011 (2011), Article ID 635926, 12 pages
http://dx.doi.org/10.1155/2011/635926
Research Article
Oscillatory Periodic Solutions for Two Differential-Difference Equations Arising in Appl... | 5 | [
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1 equation 1 unknown but still killing my brain
April 27th 2010, 07:01 PM #1
Newbie
Joined
Apr 2010
Posts
4
1 equation 1 unknown but still killing my brain
hi all. i have the following equation and am not sure how to solve it. it seems so simple but i haven't done math in a while and am not sure the step... | 4 | [
0.053466796875,
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... | 25,462 | 25462 | |
Points on horizontal tangent plane?
March 12th 2011, 03:56 PM #1
Points on horizontal tangent plane?
This is a question from my calculus 3 class.
"Find all points on the surface at which the tangent plane is horizontal."
z = x^2 - xy + y^2 - 2x + 4y
Okay, so I'm not sure where to begin. I know that ... | 4 | [
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Sensitivity Studies for the Exercise I-1 of the OECD/UAM Benchmark
Science and Technology of Nuclear Installations
Volume 2012 (2012), Article ID 817185, 10 pages
http://dx.doi.org/10.1155/2012/817185
Research Article
Sensitivity Studies for the Exercise I-1 of the OECD/UAM Benchmark
^1San Piero a Grado Nuclear Rese... | 4 | [
0.00121307373046875,
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Math Help
Hello, Mr_Green! I agree with Plato . . . If $x \;=\;\sum^6_{i=2}\ln(3i-2)$ What is the value of $e^x$ ? We have: . $x \;=\;\ln(4) + \ln(7)+\ln(10)+\ln(13)+\ln(16) \:=\:\ln\left(4\!\cdot\!7\!\cdot\!
10\!\cdot\!13\!\ cdot\!16\right) \:=\;\ln(58,240)$ Therefore: . $e^x\;=\;e^{\ln58,240} \;=\;58,240$
| 4 | [
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0.0385742... | 25,465 | 25465 | |
I need help with functions.
February 24th 2009, 11:46 AM #1
Newbie
Joined
Feb 2009
Posts
3
I need help with functions.
Can someone please help me solve these three problems:
1) Let f be the function defined by f(x) = 2x^4 + 5. Find f(a+h), f(2a-h).
2) Let f be the function defined by f(x) = -3x^... | 4 | [
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0.027099609375,
0.06396484375,
-0.0859375,
0.0007171630859375,
-0.0311279296875,
-0.0194091796875,
0.050537109375,
-0.053466796875,
... | 25,466 | 25466 | |
On Uniform Exponential Stability and Exact Admissibility of Discrete Semigroups
International Journal of Differential Equations
Volume 2013 (2013), Article ID 268309, 4 pages
http://dx.doi.org/10.1155/2013/268309
Research Article
On Uniform Exponential Stability and Exact Admissibility of Discrete Semigroups
^1Shahe... | 4 | [
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0.0179443359375,
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0.035400390625... | 25,467 | 25467 | |
Minimum Distance
October 18th 2009, 11:01 AM #1
Minimum Distance
Can somebody tell me if I've started this off right?
I need to use the Lagrange method to find the minimum distance from the point (1,2,3) to any point of the surface: $x + 2y - z = 2$
Let: $D^2=f(x,y,z)=(x-1)^2+(y-2)^2+(z-3)^2$
and
... | 5 | [
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0.0111083984375,
-0.078... | 25,468 | 25468 | |
Density-Wave Spiral Theories in the 1960s. II - I.I. Pasha
3.2. Group properties of tightly wrapped packets
...a shatteringly destructive article.
... | 4 | [
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About direct image of ideal sheaves
up vote 3 down vote favorite
Let $\mu:X'\rightarrow X$ be a birational morphism of normal complex projective varieties.
Consider the two ideal sheaves $I_1= \mu_*\mathcal{O}_{X'}(-\sum d(E)E)$, $I_2=\mu_*\mathcal{O}_{X'}(-\sum(d(E)+1)E)$, where the $d(E)$'s are non negative integer... | 5 | [
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0.05322265625,
-0... | 25,470 | 25470 | |
Taylor development
April 29th 2011, 03:43 PM #1
Member
Joined
May 2010
Posts
241
Taylor development
Hi there. I have this exercise which I'm trying to solve now. It says:
Using that $\displaystyle\sum_{n=0}^{\infty}x^n=(1-x)^{-1}$ find one Taylor development for the function $f(x)=\ln(1-x)$
So,... | 5 | [
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Integral and Series Representations of Riemann's Zeta Function and Dirichlet's Eta Function and a Medley of Related Results
Journal of Mathematics
Volume 2013 (2013), Article ID 181724, 17 pages
http://dx.doi.org/10.1155/2013/181724
Research Article
Integral and Series Representations of Riemann's Zeta Function and D... | 4 | [
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0.034423828125,
-0.0544... | 25,472 | 25472 | |
Sign-Changing Solutions for Nonlinear Elliptic Problems Depending on Parameters
International Journal of Differential Equations
Volume 2010 (2010), Article ID 536236, 33 pages
http://dx.doi.org/10.1155/2010/536236
Research Article
Sign-Changing Solutions for Nonlinear Elliptic Problems Depending on Parameters
^1I... | 5 | [
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-0.013916015625... | 25,473 | 25473 | |
shortest chord
November 10th 2010, 10:17 PM #1
Member
Joined
Mar 2008
From
???
Posts
169
shortest chord
What normal to the curve y = x^2 forms the shortest chord?
This is what I did:
I used parametric form of parabola and did stuff, put it in distance formula.. d/dt = 0 it, I'm getting a com... | 5 | [
0.005523681640625,
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0.08447265625,
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-0.03955078125,... | 25,474 | 25474 | |
Urgent help needed please!!!
June 28th 2008, 12:11 AM #1
Newbie
Joined
Jun 2008
Posts
4
Scott is saving for an overseas holiday and he is looking for the best bank in which to invest his money. Three banks are offering different interest rates as follows:
Bank Able: 8.1%(nominal p.a.) compounded mont... | 4 | [
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-0.029541015625... | 25,475 | 25475 | |
Eigenvalues
August 29th 2011, 01:36 AM #1
Member
Joined
Jan 2011
Posts
110
Eigenvalues
I am trying to determine the eigenvalues of A
A =
(6 0 2)
(0 7 0)
(2 0 3)
Which is a 3x3 matrix.
So far I have.
The characteristic equation is det (A-lambda I)=0;
|6-lam 0 2|
|0 ... | 5 | [
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0.0... | 25,476 | 25476 | |
Infinite Sequences and Series
November 13th 2008, 09:41 PM #1
Newbie
Joined
Sep 2008
Posts
7
Infinite Sequences and Series
I have to determine whether the sequence converges or diverges and, if it does converge, find the limit. I'm confused about these two.
arctan(2x)
The limit of arctan(x) as ... | 5 | [
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-0.0664... | 25,477 | 25477 | |
Please help!
May 18th 2006, 12:02 AM #1
Newbie
Joined
Mar 2006
Posts
17
Please help!
I really need someone to help me understand this very clearly:
A hemispherical bowl has an internal radius of 13 cm, and contains water to a maximum depth of 8 cm. Find the volume of water in the bowl. Show all work... | 5 | [
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Nonlinear Extension of Multiproduct Expansion Schemes and Applications to Rigid Bodies
International Journal of Differential Equations
Volume 2013 (2013), Article ID 681575, 10 pages
http://dx.doi.org/10.1155/2013/681575
Research Article
Nonlinear Extension of Multiproduct Expansion Schemes and Applications to Rigid ... | 4 | [
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IntroductionBackgroundCamera CalibrationMulti-Head Camera CalibrationMethodologyCamera Calibration with RO ConstraintsImage RectificationImage RegistrationImages FusionExperimental AssessmentConclusionsReferencesFigures and Tables
Integrating medium format cameras to produce high-resolution multispectral images is a re... | 4 | [
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Quadratic Stark Effect
Next: Degenerate Perturbation Theory Up: Time-Independent Perturbation Theory Previous: Non-Degenerate Perturbation Theory
Quadratic Stark Effect
Suppose that a one-electron atom [i.e., either a hydrogen atom, or an alkali metal atom (which possesses one valance electron orbiting outside ... | 4 | [
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[SOLVED] Find sum of infinite series?
April 23rd 2009, 05:34 AM
fardeen_gen
[SOLVED] Find sum of infinite series?
Find the sum of the following infinite series:
∑(n = 0 to ∞) (1/n![∑(k = 0 to n) ((k+1).∫(from 0 to 1) 2^(-(k +1)x) dx]8)
April 25th 2009, 09:55 PM
fardeen_gen
Is it something to do with ... | 5 | [
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0.016845703125,
-0.1357421875,
-0.0181884765625,
0.00100... | 25,482 | 25482 | |
exponents and logs
May 14th 2007, 04:48 PM
turillian@gmail.com
exponents and logs
This type of question is kiiiiiling me right now.
Solve for x.
2^(1-x) = 3
Solve for x.
3^(2x-1) = 5
EDIT: these two are similar ones I can't find a solid approach to.
log base 2 of (log base 3 of (x)) = 4
... | 4 | [
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Set - Distributive Law
June 16th 2009, 04:15 AM #1
Member
Joined
Jun 2009
Posts
78
Set - Distributive Law
I've came across an example...
By using A-B=A n B', prove that (A u B)-(A n B)=[A-(A n B)] u [B-(A n B)]
The solution they gave is...
(A u B)-(A n B)=(A u B) n (A n B)'
=[A n (A n ... | 4 | [
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Graph theory proof
September 3rd 2013, 11:21 AM
tarheelborn
Graph theory proof
Use ordinary induction on k or on the number of edges (one by one) to prove that a connected graph with 2k odd vertices composes into k trails if k > 0. Does this remain true without the
connectedness hypothesis?
So far, I ha... | 4 | [
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-0.00025... | 25,485 | 25485 | |
Convergence of sequence
April 4th 2010, 11:07 AM #1
Newbie
Joined
Apr 2010
Posts
11
Convergence of sequence
A) How do you prove that if 0(</=)x(</=)10, then 0(</=)sqrt(x+1)(</=)10?
B) So once that is found, then how can you prove that if 0(</=)u(</=)v(</=)10, then 0(</=)sqrt(u+1)(</=)sqrt(v+1)(</=)1... | 5 | [
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-0.020385... | 25,486 | 25486 | |
Fixed point in rotations
October 18th 2010, 06:07 AM #1
Fixed point in rotations
Let $P,Q \in \mathbb{E}^2$ be distinct points, and $\alpha, \beta$ angles such that $\alpha+\beta eq 0, 2 \pi$.
Let OPQO' be a quadrilateral such that $OPO'= \alpha$, $O'Qo= \beta$ are directed angles (both clockwise as interior... | 5 | [
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0.0311279296875... | 25,487 | 25487 | |
-Dimensional Mixed-Type Additive and Quadratic Functional Equation in Non-Archimedean Normed Spaces
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 401762, 9 pages
http://dx.doi.org/10.1155/2012/401762
Research Article
Stability of the -Dimensional Mixed-Type Additive and Quadratic Functional Equation in... | 5 | [
-0.055419921875,
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0.0322265625,
-0.01031494140625,
... | 25,488 | 25488 | |
Matrix of a Nilpotent Operator Proof
March 27th 2011, 02:40 PM
Anthonny
Matrix of a Nilpotent Operator Proof
I'm trying to understand this one proof about the matrix of a nilpotent operator and I'm stuck on this one part. Here is the theorem I'm trying to prove and how the proof goes:
Suppose N is a nilpote... | 4 | [
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0.04492... | 25,489 | 25489 | |
Sample Size Growth with an Increasing Number of Comparisons
Journal of Probability and Statistics
Volume 2012 (2012), Article ID 935621, 10 pages
http://dx.doi.org/10.1155/2012/935621
Research Article
Sample Size Growth with an Increasing Number of Comparisons
^1Department of Medicine, UCLA School of Medicine, Los A... | 5 | [
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A few analysis questions
December 28th 2008, 02:25 PM #1
A few analysis questions
Hey everyone! Any input would be appreciated.
A note on notation, $f\in\mathfrak{R}(\alpha)$ on $[a,b]$ means that $f$ is Riemann-Stieltjes integrable with respect to $\alpha(x)$ on the interval $[a,b]$
Question 1: Let $x_... | 5 | [
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... | 25,491 | 25491 | |
Math Help
April 13th 2008, 10:29 PM #1
Member
Joined
Feb 2008
Posts
79
Parity
With my exam on Friday, I'm trying to get all these practice probs done since some of them will be on the exam.
If $P$ is the Parity Operator, determine the parity of the functions below:
$P\sin{x} = ?$
$Pe^{-x} ... | 5 | [
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0.0234375,
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trig equations
December 5th 2012, 07:08 AM
enea54
trig equations
hi guys , i am a high school student , and i have a trigonometry test tomorrow . i would appreciate every help from you.
for now i can't solve these trigonometry equations.
they are mashing up my mind
1) sin^2x + sinx * cosx = 1
... | 4 | [
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Compound Angle Identity
March 6th 2010, 03:16 PM #1
Newbie
Joined
Jan 2010
Posts
21
Compound Angle Identity
How would I prove these identities?
1) sin(A+B)*sin(A-B)=(sin A)^2*(sin B)^2
I've gotten to expanding it to
(sin(A)cos(B)+sin(B)cos(A))*(sin(A)cos(B)-sin(B)cos(A))
then
(sin(... | 4 | [
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The Kinematics Analysis of a Novel 3-DOF Cable-Driven Wind Tunnel
Mechanism
Journal of Robotics
Volume 2010 (2010), Article ID 609391, 7 pages
http://dx.doi.org/10.1155/2010/609391
Research Article
The Kinematics Analysis of a Novel 3-DOF Cable-Driven Wind Tunnel Mechanism
^1College of Aerospace Engineering, NUAA,... | 4 | [
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0.1123046875,
-0.07568359375,... | 25,495 | 25495 | |
Solve an equation system with three unknown variables
February 27th 2011, 04:08 AM #1
Junior Member
Joined
Jan 2011
Posts
49
Solve an equation system with three unknown variables
Please solve this equation system:
xy+x+y=11
xz+x+z=14
yz+y+z=19
First I factorized everything:
(x+1)(y+1... | 4 | [
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-0.046630859375,... | 25,496 | 25496 | |
Direct Index Method of Beam Damage Location Detection Based on Difference Theory of Strain Modal Shapes and the Genetic Algorithms Application
Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 302482, 12 pages
http://dx.doi.org/10.1155/2012/302482
Research Article
Direct Index Method of Beam Damage ... | 4 | [
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0.024291992187... | 25,497 | 25497 | |
-Laplacian Integrodifferential Equations in Banach Spaces
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 398632, 9 pages
http://dx.doi.org/10.1155/2013/398632
Research Article
A Class of Fractional -Laplacian Integrodifferential Equations in Banach Spaces
^1Guangxi Key Laboratory of Hybrid Computation ... | 5 | [
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Function Integrate-Qag
(
integrate-qag
< f > < a > < b > &key (key 0) (limit 100) (epsabs 0.0d0) (epsrel 1.d-5) )
Compute the integral of f(x) from a to b.
b
/
[
I f(x) dx
]
/
a
f - double precision
function subprogam defining the integrand
function f(x). the actual name for f needs to be
a - double precision
lo... | 4 | [
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