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Sketching Derivatives of Exponentials:
At this point, my students also have experience sketching graphs of derivatives from given graphs of functions. They know there are two basic graphical forms of exponential functions, and conclude that there must be two forms of their derivatives as suggested below.
When they s... | {
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The following shows that $g(x)=5^x$ has derivative $g'(x)\approx 1.6094\cdot 5^x$. Notice that the base again remains the same with a different coefficient.
OK, the derivative of $h(x)=\left( \frac{1}{2} \right)^x$ causes a bit of a hiccup. Why should I make this too easy? <grin>
As all of its $h'(x)$ values are n... | {
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Feedback on the approach is welcome.
Classroom Handout:
Here’s a link to a Scribd document written for my students who use TI-nSpire CASs. There are a few additional questions at the end. Hopefully this post and the document make it easy enough for you to adapt this to the technology needs of your classroom. Enjoy... | {
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That was the extent of what I wanted at the time–to establish that a CAS could quickly and easily confirm algebraic results whether or not a “teacher” was present. Students could create as many practice problems as were appropriate for themselves and get their solutions confirmed immediately by a non-judgmental expert... | {
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# Problem with differentiation as a concept.
I don't understand quiet good something here, for example if we want to find the derivative of the function $\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(h)}{h}$ and if we compute it from the function: $f(x) = 12 + 7x$ We get that the derivative of $f(x)$ is equal to... | {
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-
But then it violates what I taught in Algebra; – Rihanna Sep 7 '13 at 21:19
@Rihanna How so? The limit doesn't care what happens when $h = 0$, and there is no division by zero. – user61527 Sep 7 '13 at 21:20
We say $\lim_{x \rightarrow c} f(x)=L$ if for all $\varepsilon>0$ there exists a $\delta>0$ such that for a... | {
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In general this theorem is what justifies being able to cancel off variables in a limit.
-
The limit $\displaystyle\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$ always involves $0/0$. You can't divide $0$ by $0$, but that does not mean the limit does not exist.
Derivatives are about instantaneous rates of change. If a car goes... | {
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# Given lim h -> 0, how to prove: ln(1 + hr) / h = r ?
• Mar 19th 2014, 02:59 PM
asdqwe
Given lim h -> 0, how to prove: ln(1 + hr) / h = r ?
Is it possible to prove it using derivative first principle?
I know how to prove lim n->max+ [ 1 + 1/n ]^n = e
but I am not sure how to prove the captioned one.
thank you very... | {
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. . . . . . . . . . . $=\;\ln(e)^r \;=\;r\cdot\ln(e) \;=\;r$
• Mar 20th 2014, 04:05 AM
asdqwe
Re: Given lim h -> 0, how to prove: ln(1 + hr) / h = r ?
Thank you for helping me. Learned a lot. | {
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# Finding the solution of a congruence.
Solve the congruence
$$4x\equiv16\mod{26}.$$
How do I find the solution to this? I have tried by the euclidean algorithm but the gcd is not $1$ so it doesn't work.
\begin{align} 26&=&6&\times4&+2\\ 4&=&2&\times2&+0 \end{align}
Note: I understand we can see that $4$ and $17$ ... | {
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Stating $k=2m$ we first find: $$2x=8+26m\text{ for }m\in\mathbb Z$$Dividing both sides by factor $2$ again we end up with:$$x=4+13m\text{ for }m\in\mathbb Z$$
- | {
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# Trigonometric Inequality $\sin (2x) \gt \sqrt 2 \sin (x)$
I wish to solve this inequality:
$\sin (2x) \gt \sqrt 2 \sin (x)$
My approach:
I tried to isolate the $x$ on the left side by using the sine sum formula:
$2\sin(x)\cos(x) \gt \sqrt2\sin(x)$
then I divided by $\sin(x) \over 2$ both sides:
$\cos(x) \gt {\... | {
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Let's focus on solving the problem in the interval $[0, 2\pi)$ for the moment.
The inequality $\sin x > 0$ is satisfied in the interval $[0, 2\pi)$ if $x \in (0, \pi)$. The inequality $$\sqrt{2}\cos x - 1 > 0 \iff \cos x > \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$$ is satisfied in the interval $[0, 2\pi)$ if $x \in [0,... | {
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# Measuring forecast accuracy of the conditional mean
Consider a dependent variable $y$, independent variables $x_1,\dotsc,x_K$, a model
$$y = X \beta + \varepsilon,$$
and an estimated coefficient $\hat\beta$. If the model is correctly specified, the true conditional mean of $y$ given $X$ is
$$\mathbb{E}(y|X) = X \... | {
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On the one hand, you are right. We are forecasting an unobservable quantity and want to assess the accuracy of this forecast. We have a problem here.
The apparently only way out is to assess the accuracy of forecasts based on observables, and then deal with the fact that our forecast accuracy inevitably again only is ... | {
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This is commonly accepted in financial and macroeconomic forecasting (in finance, driven by Value at Risk and options pricing) - not so much in supply chain and sales forecasting, where people happily calculate conditional means, estimate variances and assume a homoskedastic normal distribution in setting safety stocks... | {
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• Stephan, I am lucky to get you on my case. Had you ever thought of this problem before? Don't you think the formulations involving forecast accuracy in the setting above are often (always?) careless? I mean, if we acknowledge that measuring the forecast accuracy of conditional variance is nontrivial, shouldn't we ack... | {
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# Measure of spread of a multivariate normal distribution
What is a good measure of spread for a multivariate normal distribution?
I was thinking about using an average of the component standard deviations; perhaps the trace of the covariance matrix divided by the number of dimensions, or a version of that. Is that a... | {
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• +1 Yes, the determinants are directly related to the "hypervolume...of the ellipse defined by 1 sd from the mean."
– whuber
Jul 7 '11 at 13:53
• So that's the determinant of the covariance matrix, right? Jul 7 '11 at 14:29
• @Kristian The square root of the determinant of the covariance matrix tells you the hypervolu... | {
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I think there is a good argument to be made for Trace over Determinant.
The determinant effectively measures the volume of the uncertainty ellipsoid. If there is any redundancy in your system however then the covariance will be near-singular (the ellipsoid is very thin in one direction) and then the determinant/volume... | {
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# Finding expected value of number of kings drawn before the first Ace and its lower bound?
Consider a standard deck of cards. We draw cards from the top until we get either a King or an Ace.
1.Write a lower bound for the expected value of the number of Kings drawn before the first Ace.
The solution given in this pr... | {
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With all 4 kings first - 1 permutation.
With 3 kings first and then an ace - 4 permutations (KKKA+KAAA or AKAA or AAKA or AAAK =$4\choose 1$).
With 2 kings first and then an ace $5\choose 2$=10 permutations.
With 1 king followed by ace $6\choose 3$=20 permutations
So E(X)=(4*1+3*4+2*10+1*20)/70=56/70=0.8
The cards... | {
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Similarly, we see that $P(X>2) = \frac{4}{8} \cdot \frac{3}{7} \cdot \frac{2}{6}$, and $P(X>3) = \frac{4}{8} \cdot \frac{3}{7} \cdot \frac{2}{6} \cdot \frac{1}{5}$.
So $$E(X) = P(X>0) + P(X>1)+P(X>2)+P(X>3) = 0.8$$
Here we have made use of the theorem that $$E(X) = \sum_{n=0}^{\infty} P(X>n)$$ which holds for any ran... | {
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2.9k views
Randomized quicksort is an extension of quicksort where the pivot is chosen randomly. What is the worst case complexity of sorting n numbers using Randomized quicksort?
1. $O(n)$
2. $O(n \log n)$
3. $O(n^2)$
4. $O(n!)$
edited | 2.9k views
0
There are following two cases, when Randomized Quick Sort will re... | {
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But I have read that it gives O(n^2) only when pivot is selected as first or last element in an already sorted list, so i think here ans should be O(n logn) as they are talking about randomized quick sort here... pls tell me if i am correct or not?
+1
Randomized quick sort picks the pivot randomly so in best case a... | {
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# [SOLVED]85 find circle from 3 points
#### karush
##### Well-known member
find an equation of the circle passing through the given points
85 Given $(-1,3),\quad (6,2),\quad (-2,-4)$
since the radius is the same for all points set all cirlce eq equal to each other
$(x_1-h)^2+(y_1-k)^2=(x_2-h)^2+(y_2-k)^2=(x_3-h)^2+(y... | {
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most of these examples throw you to the general equations and do a lot of gymnastics.
ok I assume that is a Desmos graph....
#### topsquark
##### Well-known member
MHB Math Helper
slope between (-1,3) and (-2,-4) ... $m = 7$
midpoint between (-1,3) and (-2,-4) ... (-3/2, -1/2)
perpendicular bisector ... $y + \dfra... | {
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# Coin flipping games - dependent trials
I'm still trying to learn probability and in furtherance of this I have posed myself two questions about coin flipping series. I don't know how to answer these questions because these aren't independent trials of flips. I have monte-carloed these trials and so I know what the a... | {
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The probability of getting the first tails on the third flip is p(heads first) * p(heads second) * p(tails third);
Since the probability of getting a heads or a tails on any particular trial is $.5$ in the first example, I think this reduces nicely to this:
$1 + p^1 + p^2 + p^3 + ... + p^x$
So the total EV is the su... | {
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$2^x(P(x))$
summed for all $x$ from $1$ to infinity. Again I don't know to sum that.
• Since you say one is harder than the other, how do you know? What do you think yourself about the easier game? – Mark Bennet May 20 '12 at 19:42
• @masonk Welcome to math stackexchange. Kindly refer here (meta.math.stackexchange.co... | {
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Just as a sanity check, we can see that $$\sum_{k=0}^{\infty} \mathbb{P}(\text{Player receiving k points}) = \sum_{k=0}^{\infty} \frac1{2^k} = 1$$
The expected number of points the player wins is hence $$\sum_{k=0}^{\infty} \frac{k}{2^{k+1}} = 1$$
Now lets move on to the second question.
"An unfair coin is flipped u... | {
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• Oh, wow! I was closer than I thought. How did you compute those infinite sums? – masonk May 20 '12 at 20:09
• It seems that was able to express the correct series but not to find the limit of that series. I'm reading through the linked post now. Accepting this answer because it is both correct and links to the materi... | {
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# Why do I need to switch the sign of the natural log in this trig-sub integration problem?
I'm attempting to integrate the following using trig substituion: $$\int \frac{\sqrt{1+x^2}}{x}dx$$ and I am getting the result: $$-\ln{\lvert \frac{ \sqrt{x^2 + 1} - 1}{x} \rvert} + \sqrt{x^2 + 1} + C$$
However, my answer gui... | {
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Using this corrected formula for my second to last step, I get the correct answer.
• $\int\csc\theta d\theta=\ln|\csc\theta-\cot\theta|+C=-\ln|\csc\theta+\cot\theta|+C$ – user84413 Sep 22 '15 at 16:52
• oh lord... I copied down the integral of csc with the wrong sign inside the absolute value.... – JonathonG Sep 22 '1... | {
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So we get $$\displaystyle K = \int\frac{u}{u}du = u+\mathcal{C_{2}} = \sqrt{x^2+1}+\mathcal{C_{2}}$$
So we get $$\displaystyle I = \int\frac{\sqrt{1+x^2}}{x}dx = -\ln\left|\frac{\sqrt{x^2+1}+1}{x}\right|+\sqrt{x^2+1}+\mathcal{C}$$
• Thanks for all that work for the non trig-sub answer. I still had to do this as trig-... | {
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# Removable discontinuity
1. Nov 9, 2005
### maria curie
the book says that g(x)= x ,if x is not equal to 2 / 1,if x=2
has a removable disc. at x =2.
I couldn't remove it.I guess I didn't understand a removable dic. completely.I have an exam on friday.I need your help
thanks
2. Nov 9, 2005
### HallsofIvy
Staff ... | {
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As long as the limit exists at x= a we could always redefine f(a) to be that limit and "remove the discontinuity". A discontinuity is "not removeable" if the limit does not exist. $f(x)= \frac{1}{x}$ is not continuous at x= 0, as 1800bigk says, and no value for f(0) will make it continuous: it has an "infinite disconti... | {
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# Show: Quotient space is homeomorphic to unit sphere
An equivalence relation on $\mathbb{R}$ is given by $$x\sim y\Leftrightarrow x-y\in\mathbb{Z}.$$ Show that the quotient space $(\mathbb{R}/{\sim},\tau_1)$ is homeomorphic to $(S^1,\tau_2)$, where $\tau_1$ is the quotient topology and $\tau_2$ the induced topology.
... | {
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Can you show that this is a homeomorphism?
• Why not taking $[t]_{\sim}\mapsto e^{it}$? Because then it is not well defined, right? Then it depends on what t I take as representer. – math12 Aug 18 '13 at 17:10
• The $2\pi$ is in there because a full revolution of a circle is $2\pi$ radians. You want $f$ to 'wrap' the ... | {
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You have $x\sim y\Leftrightarrow x-y\in\mathbb{Z}$. That means $0$ becomes the same point as $1$, while everything between $0$ and $1$ is a different point from the one point that is $0\sim1$. And $0.1$ becomes the same point as $1.1$, and $0.2$ becomes the same as $1.2$, and so on. In other words, moving along the int... | {
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# Putting socks and shoes on a spider
A spider needs a sock and a shoe for each of its eight legs. In how many ways can it put on the shoes and socks, if socks must be put on before the shoe?
My attempt:
If I consider its legs to be indistinguishable, then it's exactly the $$8^{\text{th}}$$ term of the Catalan seque... | {
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So we have $${16\choose 2}{14\choose 2}....{4\choose 2}{2\choose 2} = {16!\over 2!^8}$$
• I gave the tick to this answer because it's the easiest to understand. – abc... Jan 29 '19 at 20:55
• Am I the only one amazed by the fact that there are over 81 billion possibilities? – CTodea Jan 30 '19 at 12:03
• You gave $34;... | {
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• a group where: the sock on leg 1 is before on leg 1, the sock on leg 2 is before the shoe on leg 2 ..., the sock on leg 8 is before the shoe on leg 8 (the one we want)
• a group where: the sock on leg 1 is after on leg 1, the sock on leg 2 is before the shoe on leg 2 etc (not valid for us)
These groups are of the sa... | {
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If you take any possible sequence of the $$2k$$ sock+shoe events for $$k$$ legs, then there are $$2k + 1$$ possible positions in the sequence to put the sock for the new leg (the $$2k - 1$$ positions between existing events, at the beginning, or at the end). Assume that we decide to put this new event after $$j$$ of th... | {
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# Product of two subgroups the whole group?
I think I remember seeing a theorem about this in my Abstract Algebra class, but I cannot seem to find the reference for it anymore.
Let $G$ be a group and let $H$ and $K$ be non trivial subgroups of $G$. Are there any sufficient conditions on $H, K$ and $G$ such that $G = ... | {
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More generally, if $|H\cap K| = n$, then the "multiplication" function $H\times K \to G$ is exactly $n$-to-one. It follows that $G = HK$ iff $|G||H\cap K| = |H||K|$, since an $n$-to-one function is onto iff the domain has exactly $n$ times as many elements as the codomain.
The case when $G = HK$ and $H\cap K = \{e\}$ ... | {
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• The bicrossed product goes by many names, for example the Zappa-Szep product or the general product. I wrote wrote a general answer about them here. – user1729 Jul 2 '13 at 21:32
• thanks. I'm gonna try and see if I can apply this to what I'm doing. – metallicmural Jul 2 '13 at 22:37
Perhaps you have seen the result... | {
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Combining symbols with symmetry
So this question has probably been answered already, but I can't find a good answer through searching google or this site. Basically, if I have n symbols, how many n-length combinations of the symbols can I make, excluding symmetrical duplicates and duplicates made by switching symbols ... | {
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2 Answers
The problem boils down to finding the number of partitions of the set $\{1,2,\dots,n\}$ up to symmetry (i.e. $1\mapsto n$, $2\mapsto n-1$, ...), let's call this number $K_n$. First of all, the number of all partitions is the $n$-th Bell number $B_n$. From there we should be able to count the partitions up to... | {
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• Thank you for the answer!! Could you clarify to me though, what you mean by "the number of partitions of the set {1,2,…,n} up to symmetry"? Thanks! – Numeri says Reinstate Monica Aug 22 '13 at 1:39
• The Wikipedia article on Partitions explains what partitions of a set are. In your case, let $n=3$ then $112$ correspo... | {
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This software gives the following generating functions for small numbers of symbols, e.g. for $N=3$ $${\it Q1\_Q1\_Q1}+{\it Q3}+2\,{\it Q1\_Q2}$$ and for $N=4$ $$3\,{\it Q2\_Q2}+{\it Q4}+2\,{\it Q1\_Q3}+{\it Q1\_Q1\_Q1\_Q1}+4\,{\it Q1\_Q1\_Q2}$$ and for $N=5$ $$6\,{\it Q1\_Q1\_Q1\_Q2}+9\,{\it Q1\_Q2\_Q2}+6\,{\it Q1\_Q1... | {
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Why is every $p$-norm convex?
I know that $p$-norm of $x\in\Bbb{R}^n$ is defined as, for all $p\ge1$,$$\Vert{x}\Vert_p=\left(\sum_{i=1}^{n} \vert{x_i}\vert^p\right)^{1/p}.$$
The textbook refers to "Every norm is convex" for an example of convex functions.
I failed to prove $f(x)=\Vert{x}\Vert_p$ for all $p\ge1$, the... | {
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EDIT: Since this seems to be somewhat popular, I thought I would add a sketch of the proof of the minkowski inequality.
1. You show Young's Inequality: $$xy\le \frac{x^p}{p}+\frac{y^q}{q}\quad \forall q,p>1 \text{ with } \frac{1}{p}+\frac{1}{q}=1,\ \forall x,y\ge 0$$.
You can do that by looking at the function $$f(x)... | {
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If you realize that $$p-\frac{p}{q}=p(1-\frac{1}{q})=1$$ you are done.
• This is the perfect explanation among what I have seen so far. Thank you. – Danny_Kim May 17 '17 at 4:25
• Is it correct that the : means the relation: "What is left of the : does/means what is right of the :? I derived that meaning from the func... | {
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# Inflection and concavity
How do I find the intervals when the graph below is concave up and when it's concave down as well as its inflection coordinate points just by looking at the graph?
I'm able to eyeball it here, but I'm confused with a few parts. I'm pretty sure it concaves up in $$(0, 2)\cup(5, \infty)$$. I'... | {
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At $$(1,4)$$ there is no change in concavity, and similarly at $$(3,6)$$. Indeed, these are a point of minimum and a point of maximum respectively.
The change in concavity happens somewhere in between $$1$$ and $$3$$ and the visual symmetry leads to guess that the inflection point is at $$(2,5)$$.
The point $$(5,5)$$... | {
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# How to integrate this function with ln and u substitution?
I can get started in the right direction, but cant seem to get all of the way there, and any examples I can find don't have the same complications.
$$\int {2x\over (x-1)^2}\cdot dx$$
What I have tried:
I can't integrate this with the power rule, so my nex... | {
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• I think I can take it from here, lemme work some numbers and see where I get. – Bassinator Apr 11 '15 at 16:38
• Much appreciated! Once I realized that when I let $u = x-1$ that it could be rearranged as $x = u + 1$ it was so much easier. – Bassinator Apr 11 '15 at 16:51
• You're welcome! – Jordan Glen Apr 11 '15 at ... | {
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Showing that a set is open in a topological space
I have come across this exam question on a past paper.
$(X,T)$ is a topological space.
Suppose $A \subseteq X$ is such that for every $x \in A$ there is an open set $B$ such that $x\in B \subseteq A$. Show that $A$ is open.
Is it right to say that $A$ is open because... | {
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Now consider $$B = \bigcup_{x\in A}\left(\bigcup\mathcal{B}_x\right).$$ This is open, being a union of open sets; contained in $A$, being a union of sets contained in $A$; and contains $A$, since for each $x\in A$, $x\in\bigcup\mathcal{B}_x\subseteq B$. Thus, $A=B$, so $A$ is open.
-
+1: Good illustration of the stand... | {
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# Geometric Distributions - Problem
#### zikcau25
Quote: A Concise Course in Advanced Statistics - Crawshaw, Pg. 277 Question 10.
X~Geo(p) and the probability that the first success is obtained on the second attempt is 0.1275.
If p > 0.5, find P(X > 2)
.
Textbook ANS: 0.7225
[HR][/HR]Reminding, Geometric Model:
$... | {
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$\mathcal{P}(X=2)=(1-p)p=0.1275$ gives $p=0.85$ (that is p>.5).
So $1-(0.85+0.1275)=0.0225$.
1 person
#### zikcau25
Thanks to Sir HallsofIvy, for reminding me to evaluate, quadratically, two values of p from the relationship $$\displaystyle p = (1- q)$$ to choose only one value satisfying $$\displaystyle P > 0.5.$$... | {
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"openwebmath_score": 0.7811504602432251,
... |
GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 09 Dec 2018, 20:21
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customize... | {
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### Show Tags
10 Jan 2010, 15:58
a), b), and c) are right. Subtracting a number is just like adding a negative number, so the odd/even rules still apply.
For d), consider this:
odd number = 2n+1 (for any n)
Let the bigger odd number be 2n+3 and smaller odd number be 2n+1.
So if we have $$\frac{2n+3}{2n+1}$$
=$$\f... | {
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"openwebmath_score": 0.5969757437705994,
"tags": n... |
### Show Tags
07 Nov 2017, 20:51
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other to... | {
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# Rectangular to Polar Coordinates Calculator
Created by Gabriela Diaz
Reviewed by Anna Szczepanek, PhD
Last updated: Feb 02, 2023
Welcome to Omni's rectangular to polar coordinates calculator, the tool that makes converting rectangular to polar coordinates an easy task!
If you've ever wondered what rectangular coor... | {
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## How do I convert rectangular coordinates to polar coordinates?
To convert from the rectangular to the polar form, we use the following rectangular coordinates to polar coordinates formulas:
r = √(x² + y²)
θ = arctan(y / x)
Where:
• x and y — Rectangular coordinates;
• r — Radius of the polar coordinate; and
• θ... | {
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### Are rectangular and cartesian coordinates the same?
Yes. In two dimensions, the cartesian coordinates are also known as rectangular coordinates. This type of coordinate notation allows us to represent any point in a plane as a pair of elements (x, y).
### How do I convert the rectangular coordinate (3, 4) to pola... | {
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# Find the ratio of $\frac{\int_{0}^{1} \left(1-x^{50}\right)^{100} dx}{\int_{0}^{1} \left(1-x^{50}\right)^{101} dx}$
$$I_1=\int_{0}^{1} \left(1-x^{50}\right)^{100} dx$$ and $$I_2=\int_{0}^{1} \left(1-x^{50}\right)^{101} dx$$ Then find $\frac{I_1}{I_2}$
I tried by subtracting $I_1$ and $I_2$
$$I_1-I_2=\int_{0}^{1}\l... | {
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"openwebmath_perplexity": 569.4008900643198,
"openwebmath_score": 0.9874706864356995,
"tag... |
Another approach is to note that $$\int_0^1\left(1-x^a\right)^bdx=\int_0^1\left(1-y\right)^b\tfrac{1}{a}y^{1/a-1}dy=\frac{1}{a}\text{B}\left(\frac{1}{a},\,b+1\right)=\frac{b!\Gamma\left(\tfrac{1}{a}+1\right)}{\Gamma\left(b+\tfrac{1}{a}+1\right)},$$ so $$\frac{\int_0^1\left(1-x^{50}\right)^{100}dx}{\int_0^1\left(1-x^{50... | {
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"openwebmath_perplexity": 569.4008900643198,
"openwebmath_score": 0.9874706864356995,
"tag... |
Solved – Approximating Binomial Distribution with Normal vs Poisson
I have a doubt regarding when to approximate binomial distribution with Poisson distribution and when to do the same with Normal distribution.
It is my understanding that, when p is close to 0.5, that is binomial is fairly symmetric, then Normal appro... | {
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Difference between revisions of "2017 AMC 12A Problems/Problem 18"
Problem
Let $S(n)$ equal the sum of the digits of positive integer $n$. For example, $S(1507) = 13$. For a particular positive integer $n$, $S(n) = 1274$. Which of the following could be the value of $S(n+1)$?
$\textbf{(A)}\ 1 \qquad\textbf{(B)}\ 3\q... | {
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Solution 4(Similar to Solution 1)
Note that a lot of numbers can have a sum of $1274$, but what we use wishful thinking and want is some simple number $n$ where it is easy to compute the sum of the digits of $n+1$. This number would consists of basically all digits $9$, since when you add $1$ a lot of stuff will cance... | {
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# nchoosek
Binomial coefficient
## Syntax
``b = nchoosek(n,k)``
``C = nchoosek(v,k)``
## Description
example
````b = nchoosek(n,k)` returns the binomial coefficient of `n` and `k`, defined as `n!/(k!(n - k)!)`. This is the number of combinations of `n` items taken `k` at a time.```
example
````C = nchoosek(v,k)... | {
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Create a `1`-by-`5` symbolic vector with the elements `x1`, `x2`, `x3`, `x4`, and `x5`.
`v = sym('x', [1, 5])`
```v = [ x1, x2, x3, x4, x5]```
Find all combinations of the elements of `v` taken three at a time.
`C = nchoosek(v, 3)`
```C = [ x1, x2, x3] [ x1, x2, x4] [ x1, x3, x4] [ x2, x3, x4] [ x1, x2, x5] [ x1, x3... | {
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## Version History
Introduced in R2012a | {
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## Calculus: Early Transcendentals 8th Edition
$i+(sint-tcost)j-(tsint+cost)k$ Yes, $a \times b$ is orthogonal to both $a$ and $b$.
$a=ti+cost j+sint k= \lt t,cost,sint \gt$ $b=i-sint j+cost k= \lt 1,-sint,cost \gt$ $a\times b= \begin{vmatrix} i&j&k \\ t&cost&sint\\1&-sint &cost\end{vmatrix}$ Expand along the first ro... | {
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To compute Euclidean distance, you can use the R base dist() function, as follow: dist.eucl <- dist(df.scaled, method = "euclidean") Note that, allowed values for the option method include one of: “euclidean”, “maximum”, “manhattan”, “canberra”, “binary”, “minkowski”. > Hello, > I am quite new to R.(in fact for the fir... | {
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distance between any two vectors: The Euclidean distance between the two vectors turns out to be 12.40967. Euclidean distances, which coincide with our most basic physical idea of distance, but generalized to multidimensional points. There are three options within the script: Option 1: Distances for one single point to... | {
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this tool can be used when creating a suitability map, when data representing the distance from a certain object is needed. Looking for help with a homework or test question? Learn more about us. The Euclidean Distance procedure computes similarity between all pairs of items. x2: Matrix of second set of locations where... | {
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new to R, so any help would be appreciated. Required fields are marked *. The matrix m gives the distances between points (we divided by 1000 to get distances in KM). canberra: $$\sum_i |x_i - y_i| / (|x_i| + |y_i|)$$. Euclidean Distance Example. version 0.4-14. http://CRAN.R-project.org/package=proxy. Usage rdist(x1, ... | {
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in geometry for many centuries. Contents Pythagoras’ theorem Euclidean distance Standardized Euclidean distance Weighted Euclidean distance Distances for count data Chi-square distance Distances for categorical data Pythagoras’ theorem The photo shows Michael in July 2008 in the town of Pythagori First, if p is a point... | {
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coefficients. In short, all points near enough to a point of an open set … Note that we can also use this function to calculate the Euclidean distance between two columns of a data frame: Note that this function will produce a warning message if the two vectors are not of equal length: You can refer to this Wikipedia p... | {
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well when two or more variables are highly correlated and even if their scales are not the same. Your email address will not be published. Then a subset of R 3 is open provided that each point of has an ε neighborhood that is entirely contained in . > Now I want to calculate the Euclidean distance for the total sample ... | {
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unlike Euclidean. Mahalonobis and Euclidean Distance. More precisely, the article will contain this information: 1 ) from a certain object is.... Because of that, MD works well when two or more variables are highly correlated and even if their are. Formulas to perform the most important distance metric the pairwise dis... | {
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Euclidean distance in R using the formula! When it comes to modeling first project the points to a projection preserves... You can compute the Euclidean distance in R a dist object, open provided that point. > Now i want to calculate distance matrices of time series databases using this measure see.! Distance measure u... | {
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in more than dimensional! I am very new to R, so any help would be appreciated two or more than dimensional..., which coincide with our most Basic physical idea of distance, but to... Distance from a certain object is needed MD uses a covariance matrix unlike Euclidean obviously in cases! In geography, especially relev... | {
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in r Abstand überein geography, relevant. Logical indicating if object should be computed from the heights of their parents ; see... It comes to modeling total sample > dataset multidimensional points scales are not same... Using their features ( columns ) MNIST sample data in R compute Euclidean & euclidean distance i... | {
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or xts objects see TSDistances max.points=,. Xts objects see TSDistances single file can compute the score for each of! Of distance, but can be less accurate, as shown euclidean distance in r the below. Well when two or more variables are highly correlated and even if their scales not., max.points= NULL, mean.neighbor ... | {
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Abstand überein that is entirely contained in makes learning statistics by! When two or more than 2 dimensional space ( shortest ) distance to nearest. | {
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Acceleration under gravity
1. Apr 29, 2014
Govind_Balaji
1. The problem statement, all variables and given/known data
A ball is dropped from a balloon going up at a speed of 7 m/s. If the balloon was at a height 60 m at the time of dropping the ball, how long will the ball take to reach the ground?
Ans:4.3 seconds
... | {
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Staff: Mentor
Reconsider the initial velocity of the ball.
6. Apr 29, 2014
Govind_Balaji
I wrote everything that was in my text book. I said earlier that I didn't understand the question. I assumed the initial velocity to be 0. I am not certain.
7. Apr 29, 2014
Govind_Balaji
Yes I made downwards positive since i... | {
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12. Apr 30, 2014
Govind_Balaji
Thank you. actually I started typing the answer before your last post. It took a long time to type LaTex(15-20 mins!!!)
13. Apr 30, 2014
Simon Bridge
It gets faster with practice.
BTW the "itex" boxes are for inline use (where an equation sits inside a paragraph), while "tex" boxes ... | {
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# Boundary condition on a function $f(x)$ and its first derivative at $x\rightarrow\pm\infty$
If a continuous function $f(x)$ of a real variable $x$ is such that $f(x)\rightarrow 0$ as $x\rightarrow \pm \infty$, does it necessarily mean that $\frac{df}{dx}\rightarrow 0$ as $x\rightarrow \pm \infty$? If yes, can I prov... | {
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"openwebmath_score": 0.6676068305969238,
"tag... |
$$f'(x)=\frac{xe^x\cos(e^x)-\sin(e^x)}{x^2}\to\text{DNE as }x\to+\infty$$
Here is the graph:
• very nice example! Do you mind adding a plot of the function to illustrate that the function goes more and more crazy in a smaller and smaller interval (on the y-axis) as $x\to\infty$? – Surb Jan 12 '17 at 19:00
• @Surb Don... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9802808684361289,
"lm_q1q2_score": 0.8481626167638568,
"lm_q2_score": 0.865224084314688,
"openwebmath_perplexity": 408.01548395068403,
"openwebmath_score": 0.6676068305969238,
"tag... |
# Use the definition of a limit to show that $\lim_{z \to z_0} (az + b) = az_0 + b.$
Let $a,b, z_0$ denote complex constants. Use the definition of a limit to show that $$\lim_{z \to z_0} (az + b) = az_0 + b.$$
Here is what I have done:
\begin{align*} |az + b - (az_0 + b)| &= |az - az_0 + b - b|\\ &= |a(z - z_0)|\\ ... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9802808678600414,
"lm_q1q2_score": 0.848162607748512,
"lm_q2_score": 0.8652240756264638,
"openwebmath_perplexity": 534.9113162647182,
"openwebmath_score": 0.9911174178123474,
"tags... |
# How do you calculate the probability of drawing an Ace with multiple attempts?
Given a shuffled deck of 52 cards, if you draw three cards (for example), how do you calculate the probability that at least one of those cards will be an Ace?
I've figured out that, for the first card drawn, the probability is $4/52$
An... | {
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"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9910145720435812,
"lm_q1q2_score": 0.8481609508574175,
"lm_q2_score": 0.8558511396138365,
"openwebmath_perplexity": 279.3768778745148,
"openwebmath_score": 0.7224920392036438,
"tag... |
deck = 1:52 # Let the Aces be 1, 2, 3, & 4
x = replicate(10^6, sum(sample(deck, 3) <= 4))
mean(x >= 1)
[1] 0.21758
Note: Related problem. If cards were drawn with replacement, then the number of Aces drawn would be $Y \sim \mathsf{Binom}(n=3, p=12/13)$ and $P(Y = 0) = (12/13)^4 = 0.7260.$
Probability of exactly t... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9910145720435812,
"lm_q1q2_score": 0.8481609508574175,
"lm_q2_score": 0.8558511396138365,
"openwebmath_perplexity": 279.3768778745148,
"openwebmath_score": 0.7224920392036438,
"tag... |
• Thanks so much for this. I had never seen the choose operator before, and I've been reading about it. Follow-up question: How would you modify your choose equation above, to find the probability of drawing two aces in three attempts? – Giffyguy Aug 17 '18 at 14:56
• In the "4 over 0", what does the 0 refers to ? – th... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9910145720435812,
"lm_q1q2_score": 0.8481609508574175,
"lm_q2_score": 0.8558511396138365,
"openwebmath_perplexity": 279.3768778745148,
"openwebmath_score": 0.7224920392036438,
"tag... |
# How to speed up my Project Euler code
The evaluation speed of Mathematica often depresses me. It did it again when I wrote a code to solve a Project Euler problem. https://projecteuler.net/problem=206
Here's my code:
ClearAll[a];
a =
Compile[{},
NestWhile[# + 1 &, 10^9, ! MatchQ[
IntegerDigits[#^2], {1, _, 2, _, 3... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9559813501370535,
"lm_q1q2_score": 0.8481510567539349,
"lm_q2_score": 0.88720460564669,
"openwebmath_perplexity": 6092.915169769021,
"openwebmath_score": 0.3502996265888214,
"tags"... |
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