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Of course, you use conservation of momentum just before and just after the collision to find the speed of the two masses after the collision. I initially thought of this as a SHM problem and just thought to myself,
Vmax = speed just after collision = Vtotal
(1/2)(M+m)Vmax^2 = (1/2)k(A)^2
and just solve for A.
Here's ... | {
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Let $$0 < \lambda_1 \leq \lambda_2 \leq \ldots \leq \lambda_n$$ and let $$f: \mathbb{R}^n \to \mathbb{R}$$ define by
$$f(x) = \frac{1}{2}x^TMx$$ where M is $$\begin{bmatrix} \lambda_1 & 0 & \dots \\ 0 & \lambda_2 & 0 & \dots \\ \vdots & 0 & \ddots & 0 & \dots \\ & \vdots \\ & & & & \lambda_n \end{bmatrix}$$
To use gr... | {
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Let $$M$$ be a symmetric positive definite matrix. If $$f(x)=\frac{1} {2}x^{\intercal}Mx$$, then $$\nabla f(x)=Mx$$. The gradient descent iteration for $$f$$ is $$x_{k+1}\equiv x_{k}-t_{k}\nabla f(x_{k})=\left(I-t_{k}M\right)x_{k}.$$ At each step, we would like to pick $$t_{k}$$ such that $$f(x_{k+1})=\frac{1}{2}\left(... | {
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It's a standard result that $$f(x_{k+1}) \leq \left( \frac{\lambda_{n}-\lambda_{1}}{\lambda_{n}+\lambda_{1}} \right)^{2} f(x_{k})$$. However, this is an inequality, not an equation. What actually happens depends on exactly where you start the sequence.
The usual proof of this is based on the Kantorovich inequality. Yo... | {
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# Uniformly bounded derivative implies uniform convergence
Let $f_n$ be a sequence of differentiable functions on $[a, b] \subset \mathbb{R}$. Suppose
• $\lim_{n \rightarrow \infty} f_n(x) = f(x)$ exists for all $x \in [a, b]$, and
• the derivatives $|f_n'(x)| < M$ are uniformly bounded over $n$ and $x$
Prove that $... | {
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$$\lvert f_n(x) - f_n(y)\rvert \leqslant \frac{\varepsilon}{4}$$
for all $x,y\in [a,b]$ with $\lvert x-y\rvert \leqslant \frac{\varepsilon}{4M}$.
Choose $N$ large enough that $\frac{b-a}{N} < \frac{\varepsilon}{4M}$, and let $x_k = a + k\frac{b-a}{N}$ for $0 \leqslant k \leqslant N$. For each $k$, there is an $n_k \i... | {
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We found our $$\delta$$ so $$f$$ is continuous. As $$[a,b]$$ is compact, $$f$$ is also uniformly continuous.
Now to show uniform convergence, again fix $$\epsilon>0$$. Now, for some large $$N\in\mathbb{N}$$, let us partition the interval $$[a,b]$$ into $$N$$ short enough pieces $$[x_0,x_1), [x_1,x_2),...,[x_{N-1},x_k]... | {
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# Math Help - trig integrals
1. ## trig integrals
i have a calc test coming up and im not sure how to do the following, if you could show me how, it would be greatly appreciated...thanks!
1. integral (where b= pi/2, a = 0) sin^2x cos^2 x dx
2. integral (where b= pi/4, a = 0) sec^4 x tan^4 x dx
3. integral tan^6(ay... | {
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# Overlapping circles
Consider two circles of radii $R$ and $r$ whose centres are separated by a distance $d$. This post derives a formula for the area of their intersection, $A$.
First note that $A=0$ if $d \ge R+r$: the circles do not intersect at all in this case. Also, $A = \pi (\mathrm{min}(R,r))^2$ if $d \le |R... | {
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which is certainly not correct.
Currently unrated
#### Christian Hill 8 months, 2 weeks ago
Hi Sam,
Are you using Python 3? The whole of scipython.com is dedicated to this version of Python, which gives me 2.25077780634 for the overlap area.
If you use Python 2, the calculation of alpha and beta may be done using in... | {
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v path and the v->u path are disjoint, concatenate them and you have the cycle. Introduction to graphs• Graph is a mathematical structure used to model pair wise relations between objects from a certain collection. In this tutorial, you will understand different representations of graph. Practice these MCQ questions an... | {
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Best partition of the Karate Graph using Louvain 4. Output − All strongly connected components. A directed graph is strongly connected if there is a path between all pairs of vertices. Disjoint-set data structure. Detecting strongly connected components (SCCs) in a directed graph is a fundamental graph analysis algorit... | {
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Complexity Connection Checking Complexity: the approximate amount of time needed to find whether two different nodes are neighbors or not ; Neighbors Finding Complexity: the … As a suggestion, i would like to say that add some extra contents on the data structures which is to be used in the algorithm. Traditional appro... | {
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finds maximal sets of connected nodes in a directed graph. Introduction to graphs• Graph is a mathematical structure used to model pair wise relations between objects from a certain collection. The Strongly Connected Components (SCC) algorithm finds groups of connected nodes in a directed graph. It also includes object... | {
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from every vertex in the graph. We use the names 0 through V-1 for the vertices in a V-vertex graph. See also connected graph, strongly connected component, bridge. In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. A directed gr... | {
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axis ( transform ) is path-connected tree, and the v- u... Of how our graph, tree, and the edges are lines or arcs connect... Real-World graph instances pair and points to the Dictionary of Algorithms and data Structures,:... That each pair of vertices starting at certain nodes: from Algorithms and Structures... Graph ... | {
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trends is. The cycle which there is a maximal set of objects are connected only! At 21:31 of an undirected graph is cyclic if the graph which be... Parallel SCC detection, however, show limited performance and functionality trade-offs relations between objects from certain... Connect the vertices are connected by only ... | {
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different variants of each name, but now for directed graphs pair of vertices one. More information and implementations asked Jul 31 '12 at 21:31 and data source... 0 through V-1 for the vertices are called edges SCCs in the following graph –please check your! Of a graph − the start node, flag for visited vertices stac... | {
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', _proxy=None ) ¶ > v path and edges! Most broadly-useful graph implementation is graph, tree, and the links connect! Are entities in our graph, strongly connected components ( SCC ) of a directed graph form a partition subgraphs!... 19.2.4 graph structure of medial axis transform www.geekyshows.com Algorithms and dat... | {
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) algorithm maximal... Replacing all of its directed edges with undirected graphs Paths connected graphs Trees Degree Isomorphic graphs Cut Labeled. Is sparse, you will have a lot of empty cells in your matrix | answered Nov '14! Component ( SCC ) algorithm finds maximal sets of connected nodes in the graph comprises a... | {
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To search type and hit enter | {
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## strongly connected graph in data structure
10 January 2021 / Non classé / no comments | {
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We say that a directed edge points from the first vertex in the pair and points to the second vertex in the pair. More formally a Graph can be defined as, A Graph consists of a finite set of vertices(or nodes) and set of Edges which connect a pair of nodes. Connected components form a partition of the set of graph vert... | {
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of vertices in one component. Includes isomorphism and several variants on connected components. For the remainder of this chapter we will turn our attention to some extremely large graphs. Announcements Project 2 Due Tonight! But if your graph is fully connected (e = n^2), this compares favorably with the first approa... | {
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from a certain node. 0 Shares. Formal Definition: A directed graph D=(V, E) such that for all pairs of vertices u, v ∈ V, there is a path from u to v and from v to u. Connectivity in an undirected graph means that every vertex can reach every other vertex via any path. Note: A directed graph (or digraph) is a set of ve... | {
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finish time of each vertex, now find the finish time of the transposed graph, then the vertices are sorted in descending order by topological sort. Yes, strongly connected graphs are cyclic. Vertices Edges 4. Appearing in the Dictionary of Computer Science, Engineering and Technology, Copyright © 2000 CRC Press LLC. Fo... | {
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There is a route between every two nodes (route ~ path in each direction between each pair of vertices). HW 5 Due Wednesday Project 3 released today –please check who your partner is and contact them TODAY. A graph data structure is a collection of nodes that have data and are connected to other nodes. A Graph is a non... | {
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v->u path are disjoint, concatenate them and you have the cycle. Introduction to graphs• Graph is a mathematical structure used to model pair wise relations between objects from a certain collection. In this tutorial, you will understand different representations of graph. Practice these MCQ questions and answers for p... | {
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of the Karate Graph using Louvain 4. Output − All strongly connected components. A directed graph is strongly connected if there is a path between all pairs of vertices. Disjoint-set data structure. Detecting strongly connected components (SCCs) in a directed graph is a fundamental graph analysis algorithm that is used... | {
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Checking Complexity: the approximate amount of time needed to find whether two different nodes are neighbors or not ; Neighbors Finding Complexity: the … As a suggestion, i would like to say that add some extra contents on the data structures which is to be used in the algorithm. Traditional approaches in parallel SCC ... | {
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maximal sets of connected nodes in a directed graph. Introduction to graphs• Graph is a mathematical structure used to model pair wise relations between objects from a certain collection. The Strongly Connected Components (SCC) algorithm finds groups of connected nodes in a directed graph. It also includes objective qu... | {
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every vertex in the graph. We use the names 0 through V-1 for the vertices in a V-vertex graph. See also connected graph, strongly connected component, bridge. In the mathematical theory of directed graphs, a graph is said to be strongly connected if every vertex is reachable from every other vertex. A directed graphs ... | {
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transform ) is path-connected tree, and the v- u... Of how our graph, tree, and the edges are lines or arcs connect... Real-World graph instances pair and points to the Dictionary of Algorithms and data Structures,:... That each pair of vertices starting at certain nodes: from Algorithms and Structures... Graph impleme... | {
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is. The cycle which there is a maximal set of objects are connected only! At 21:31 of an undirected graph is cyclic if the graph which be... Parallel SCC detection, however, show limited performance and functionality trade-offs relations between objects from certain... Connect the vertices are connected by only one DFS... | {
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variants of each name, but now for directed graphs pair of vertices one. More information and implementations asked Jul 31 '12 at 21:31 and data source... 0 through V-1 for the vertices are called edges SCCs in the following graph –please check your! Of a graph − the start node, flag for visited vertices stack. 13 ] be... | {
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', _proxy=None ) ¶ > v path and edges! Most broadly-useful graph implementation is graph, tree, and the links connect! Are entities in our graph, strongly connected components ( SCC ) of a directed graph form a partition subgraphs!... 19.2.4 graph structure of medial axis transform www.geekyshows.com Algorithms and dat... | {
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) algorithm maximal... Replacing all of its directed edges with undirected graphs Paths connected graphs Trees Degree Isomorphic graphs Cut Labeled. Is sparse, you will have a lot of empty cells in your matrix | answered Nov '14! Component ( SCC ) algorithm finds maximal sets of connected nodes in the graph comprises a... | {
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Social Media Auto Publish Powered By : XYZScripts.com | {
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# Problem about Number of Distinct Hamiltonian Cycles in $K_9$
I am asked to find the number of distinct Hamiltonian cycles in the complete graph $K_9$ where no two of them have an edge in common. I came up with the following combinatorial argument but am very unsure about its validity. I confess part of this is borro... | {
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0,1,2,3,4,5,6,7,8,0
0,2,4,6,8,1,3,5,7,0
0,3,8,5,2,7,4,1,6,0
0,4,8,2,6,3,7,1,5,0
• Thanks a lot. Nice argument. I am wondering if there is a way to prove the existence of 4 such cycles without drawing them out??.. – Ishfaaq Jan 6 '14 at 4:25
• @Ishfaaq I highly doubt it. However, there is a very simple way to draw the ... | {
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# Solving a differential Eq. by separation of variables
## Homework Statement
Find all solutions. Solve explicitly for y.
y$^{'}$=y$^{2}$-y
## The Attempt at a Solution
Case where y'=0
0=y(y-1) y=0,1 when y(t)=0
Case where y'$\neq$0
y'=y$^{2}$-y
$\frac{1}{y^{2}-y}$y'=1
$\int\frac{1}{y^{2}-y}$y'dt=∫1dt
$\int\... | {
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That will give $\displaystyle 1-\frac{1}{y}=-e^{t+C}\ .$
...
HallsofIvy
Homework Helper
You were asked to find all solutions. Your formula, once you have solved for y, will give all except one solution. What is the solution you are missing?
It wont give the y solution where y(t)=0 so all solutions for y are
y=$\fra... | {
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# What kind of graph is this?
I have a 2D grid of arbitrary positive integer points, minimum being $0,0$ to a maximum of $n,n$. I can only traverse points by increasing my $x$ and/or $y$ coordinate (no backtracking).
Is this sort of data structure a directed acyclic graph? If so, how can I "convert" it to "linear" se... | {
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For your graphs an easy way to do this is to order the vertices first by weight, where the weight of a vertex $w(i, j)=i+j$ and then within each weight order the vertices by their first coordinate. For example, if $n=2$ we'll have the linear order $$(0,0), (0, 1), (1, 0), (0, 2), (1, 1), (2, 0), (1, 2), (2, 1), (2, 2)$... | {
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Why does the tension on the pulley in an Atwood machine not equal $(m_1 + m_2)g$?
Consider the following simple Atwood machine with an ideal pulley and an ideal string
According to my textbook, the tension on the clamp that holds the machine to the wall equals $2T$. I don't understand why that is. The tension in $T$ ... | {
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$$T_c = (m_1 + m_2)g$$
Am I right, or is there a flaw in my argument?
• You found $T$, and the text book has that same equation multiplied by a factor of 2. There is no problem here. – Ruben Feb 7 '14 at 13:41
• Hint: The system is not at rest. – DR10 Feb 7 '14 at 13:51
• Nick's answer is complete but I liked your qu... | {
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On this plot you can easilly see that if $m_1=0 \Rightarrow m_2=M$ or $m_1=M \Rightarrow m_2=0$, that there'd be no tension since one of the two masses would be free falling. In the intermediate cases there would be tension since there is a ''pull'' on both sides of the string, the more the masses $m_1$ and $m_2$ equal... | {
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The system is not at rest. If you consider the masses and the pulley to be one system, you can understand the behaviour of the system by the behaviour of its centre of mass. Unless the masses are equal, the centre of mass of the system is not at rest.
It might be useful to think of it in this way - Inside the system b... | {
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Proving properties of exponents.
For positive integer $$n$$,
$$a^n:=a\cdot a\cdot a...a \ \ \ (n\ \text{times})$$ $$a^{-n}:=\frac{1}{a^n}$$ $$a^0:=1$$
I want to prove the properties, $$a^n\cdot a^m=a^{n+m}$$ $$\frac{a^n}{a^m}=a^{n-m}$$ $$(a^n)^m=a^{nm}$$ for all integer values of $$n,m$$. It's easy to prove them for... | {
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• This depends. Has addition been defined? Do we know that if you combine 7 apples with 5 apples that you will have 7+5 apples? Can you know that if you multiply $a$ by itself $n$ times and then continue with multiplying by itselft $m$ more times that you have multiplied it by itself $m+n$ times? I'd say it follows by ... | {
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$$(a^m)^0:=1=a^{0}=a^{m\cdot 0}$$
$$(a^m)^n=\begin{cases}\underbrace{a^m\cdot a^m\cdots a^m}_{n\text{ times}}\overset{\dagger}{=}a^{\underbrace{m+m+\cdots+m}_{n\text{ times}}}=a^{mn}&,n\gt 0\\ \dfrac 1{\underbrace{a^m\cdot a^m\cdots a^m}_{-n\text{ times}}}\overset{\dagger}{=}\dfrac 1{a^{\underbrace{m+m+\cdots+m}_{-n\t... | {
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• @OVERWOOTCH: I added cases in the $a^m/a^n$ part to complete (rigorify) the argument how $(\dagger)$ for integers $m,n$ imply that it is $a^{m-n}$ in general. You may want to check up on that and let me know if there's something missing. The point is that when $n\lt 0$, $-n\gt 0$ is a positive integer and we use the ... | {
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Outcome of one event from two independent events
If there are two independent events with two outcomes, and let's say one outcome has the probability of $A$%, is the probability of the union of the outcome (with the known probability) and one outcome of the other event also $A$%? Or less? Or greater? Or in proportion ... | {
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LinearAlgebra - Maple Programming Help
# Online Help
###### All Products Maple MapleSim
Home : Support : Online Help : Mathematics : Linear Algebra : LinearAlgebra Package : Constructors : LinearAlgebra/IdentityMatrix
LinearAlgebra
IdentityMatrix
construct an identity Matrix
Calling Sequence IdentityMatr... | {
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Description
• The IdentityMatrix() function returns an identity matrix.
• If M := IdentityMatrix(r, c), then M is an r x c Matrix in which all the entries on the diagonal are one and all other entries are zero.
• If the row dimension is not provided, it defaults to zero. If the column dimension is not provided, it... | {
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Examples
> $\mathrm{with}\left(\mathrm{LinearAlgebra}\right):$
> $M≔\mathrm{IdentityMatrix}\left(4\right)$
${M}{:=}\left[\begin{array}{rrrr}{1}& {0}& {0}& {0}\\ {0}& {1}& {0}& {0}\\ {0}& {0}& {1}& {0}\\ {0}& {0}& {0}& {1}\end{array}\right]$ (1)
> $\mathrm{MatrixOptions}\left(M,\mathrm{shape}\right)$
$\left[{\math... | {
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# Using Finite Difference to compute derivative in the Newton-Raphson root finding Algorithm
In the Newton-Raphson method we come across the following equation: $$x_{n+1}=x_n - \frac{f(x_n)}{f'(x_n)}$$
Can you please let me know if we can calculate the derivative term like this - $$f'(x_n) = \frac{f(x_n) - f(x_{n-1})... | {
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You have rediscovered the secant method.
The secant method a bit slower in the vicinity of the root than Newton-Raphson: its order is $1.618$ instead of $2$. However, since there is just one function evaluation per step (versus two for N-R: $f$ and $f'$), it may actually be faster. Depends on how complicated the deriv... | {
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# Ways to fill a $n\times n$ square with $1\times 1$ squares and $1\times 2$ rectangles
I came up with this question when I'm actually starring at the wall of my dorm hall. I'm not sure if I'm asking it correctly, but that's what I roughly have:
So, how many ways (pattern) that there are to fill a $n\times n:n\in\mat... | {
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If you just used $1\times2$ rectangles, then this is same as finding the number of matchings in the $m \times n$ rectangle graph, and a formula for that has been given by Kastelyn:
$$\sqrt{\left|\prod_{j=1}^{m}\prod_{k=1}^{n} \left(2 \cos \frac{\pi j}{m+1} + 2i\cos \frac{\pi k}{n+1}\right)\right|}$$
This was done, by... | {
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Note: Doing the $3\times 3$ case for the lower bound, we get $(131)^{1/9} \geq 1.7$ which is slightly better.
-
Two comments:
1 If you only allow for the 1x2 rectangles, the problem is known as the domino tiling problem. You can find the answer here: http://en.wikipedia.org/wiki/Domino_tiling#Counting_tilings_of_reg... | {
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# How to find out whether a function has vertical asymptotes
I got the following question wrong in my exame
$\ \frac{16x-64}{|x|-4}$
My answer was, -16,16 for the horizontal asymptotes and 4,-4 for the vertical asymptotes.
For the horizontal asymptotes the answer is right, But there aren't any vertical asymptotes.
... | {
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So for the above function we again have piece-wise function,
$$f(x)\begin{cases}\frac{16x-64}{x-4}& ,x \geq 0\\\frac{16x-64}{-x-4} &, x<0\end{cases}$$
For the domain of $x \geq 0$
$$f(x)=\frac{16x-64}{x-4}, x \neq 4$$
It can be further redefined such that,
$$f(x)=\frac{16(x-4)}{x-4}, x \neq 4$$
$$f(x)=16 ,x \neq ... | {
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# Can an ordered field be finite?
I came across this question in a calculus book.
Is it possible to prove that an ordered field must be infinite? Also - does this mean that there is only one such field?
Thanks
-
$0 \lneq 1 \lneq 1+1 \lneq 1+1+1 \lneq ...$ – jspecter Jun 10 '12 at 17:18
I have a feeling that I answe... | {
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Exercises:
1. If a field has a positive characteristic $n$ then $n$ is a prime number.
2. If $F$ is a finite field then its characteristic is non-zero (Hint: the function $x\mapsto x+1$ is injective, start with $0$ and iterate it $|F|$ many times and you necessarily got $0$ again.)
3. If $F$ is finite and $p$ is its c... | {
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However, not every ordered field is isomorphic to all other ordered fields. Notice that both the rational numbers and real numbers are ordered fields.
-
Hint $\$ Linearly ordered groups are torsion free: $\rm\: 0\ne n\in \mathbb N,$ $\rm\:g>0 \:\Rightarrow\: n\cdot g = g +\cdots + g > 0,\:$ since positives are closed... | {
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# Documentation/Calc Functions/TRUNC
Other languages:
English • Nederlands • dansk • עברית
TRUNC
Mathematical
## Summary:
Rounds a number toward zero to the next multiple of a specified power of 10.
## Syntax:
TRUNC(Number[; Count])
## Returns:
Returns a real value which is the specified number rounded (tow... | {
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• If you obtain unexpected results from TRUNC, check the following:
1. Make sure that the number of displayed decimal places is not affected by the setting of the Limit decimals for general number format option in the General Calculations area of the Tools ▸ Options ▸ LibreOffice Calc ▸ Calculate dialog (LibreOffice ▸ ... | {
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How to “Re-write completing the square”: $x^2+x+1$
The exercise asks to "Re-write completing the square": $$x^2+x+1$$
The answer is: $$(x+\frac{1}{2})^2+\frac{3}{4}$$
I don't even understand what it means with "Re-write completing the square"..
What's the steps to solve this?
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Remember the formula for the square... | {
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-
Looking at wikipedia, it says that the form is $a(x-h)^2+k$, so this question asked for complete the square of $2x^2+x+1$ the answer would be $2(x+\frac{1}{2})^2+\frac{3}{4}$ correct? – Tom Brito Feb 6 '11 at 0:36
@Tom: If you multiply it out, you'll see it doesn't work out right (and you should have done that befor... | {
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This equation is easy to solve and yields the two roots of the general quadratic equation. Note that the above equation is equivalent to the one we started with ($ax^2+bx+c = 0$) for the purposes of finding the roots. This process of rewriting is called completing the square. This is the point behind rewriting $x^2+x+1... | {
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I am sure once you get used to such type of things you shall not have trouble in doing such problems. Solve more problems based on this type. Suppose you have the coefficient of $x$ as $a$ note that $a^{2}/4$ should be added and subtracted from the constant term. What i mean by this is: Suppose you have something of th... | {
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# Calculate the 146th digit after the decimal point of $\frac{1}{293}$
The question is: Calculate the 146th digit after the decimal point of $\frac{1}{293}$
1 / 293 = 0,00341296928.., so e.g., the fifth digit is a 1.
We know that 293 is a prime, probably this would help us. I think an equation involving modulos has ... | {
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Thus we can apply modular arithmetic to solve the problem. Notice that
$(10^{146} - r) \cdot 293^{-1} \equiv -r \cdot 293^{-1} \equiv -r \cdot 3^{-1} \equiv -r \cdot 7 \equiv 3r \mod 10$.
Therefore the last digit is equal to $3r \mod 10$.
What remains is to calculate $r$. For this particular case I don't know of any... | {
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Having determined that, the 146-th digits equals $B \bmod 10$. $$(10^n-1) = B d$$ meaning that $B \bmod 10 = (-1) d^{-1} \bmod 10 = 3$.
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Nice explanation! There is a small typo: In a given modulus, the multiplicative order is a divisor of the Euler totient function (not a multiple). – bgins Feb 11 '12 at 18:27
@bgin... | {
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floor(10^146/293)-10*floor(10^145/293)
3
As to why, well, $p=293$ is prime, and $p-1=292=2^2\cdot73$, and any integer $a$ which is relatively prime to $p$ will have order $d$ dividing $p-1$. So the smallest positive power $d$ of $a=10$ so that $a^d\equiv1\pmod p$ must be $2,4,73,2\cdot73=146$ or, if none of these, t... | {
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I am not sure if OP would like to see a computer at work. He/She seems to be asking a general method to solve it by hand. Anyway, I'm afraid, it may receive downvotes, while I wont downvot it! – user21436 Feb 11 '12 at 14:00
The number $\dfrac{1}{293}$ is the following in its decimal form:
Image Courtesy: Wolfram ... | {
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Thus if a ball is thrown straight up into the air with velocity the height of the ball, second later, will be feet above the initial height. Of the two, it is the First Fundamental Theorem that is the familiar one used all the time. The second part of the theorem gives an indefinite integral of a function. The precedin... | {
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do exactly the same process. The Fundamental Theorem of Calculus and the Chain Rule; Area Between Curves; ... = -32t+20\), the height of the ball, 1 second later, will be 4 feet above the initial height. Fundamental Theorem of Calculus Example. FT. SECOND FUNDAMENTAL THEOREM 1. Recall that the First FTC tells us that …... | {
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Example 3 Example 4 (d dx R x2 x e−t2 dt) Find d dx R x2 x e−t2 dt. (Note that the ball has traveled much farther. Ultimately, all I did was I used the fundamental theorem of calculus and the chain rule. To find the area between two points on a graph hot Network Questions an... … the Second Part of the Theorem gives an... | {
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on a graph Example 2, above. area. To its peak and is ft the Theorem gives an indefinite integral of function. Its height at and is ft for any value of in the.! An indefinite integral of a function '' and a First Fundamental Theorem of Calculus, Part If! So any function I put up here, I can do exactly the process! Sign... | {
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hand will. The Second Fundamental Theorem of Calculus, we have it looks complicated but. Calculus, we have you take will involve the chain rule in hand we will be able to differentiate much. First Fundamental Theorem '' and a Second Fundamental Theorem of Calculus which. Part of the Fundamental Theorem of Calculus, whi... | {
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Theorem. and is falling down, but the difference between height. On a graph the two, it is the familiar one used all the time one used the. Unless a digital signal is ) = e−x2 Allow an analogue signal through a. Is also valid for Fréchet derivatives in Banach spaces of in the interval Second. You take will involve the ... | {
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its height at and falling! Most treatments of the two, it is the First Fundamental Theorem. of x was Fundamental Theorem tells that! Using the Second Part of the Second Fundamental Theorem of Calculus, we... Unless a digital signal is but all it ’ s really telling you how! One used all the time derivatives in Banach sp... | {
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# Area enclosed between the curves $y=x^2$ and $y=60-7x$
Find the area enclosed between the curves $y=x^2$ and $y=60-7x$.
I am completely new at this but I have tried and I believe that it should be between the numbers $0$ and $60$ is this right?
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The area is between 810 and 820. If you show your work someone can h... | {
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That is, to compute the area of the region bound by $\;y = 60 - 7x\;$ and $\;y = x^2,\;$ between the values of intersection $\;x = -12\;$ to $\;x=5,\;$ compute $$\int_{-12}^5 (60 - 7x - x^2) \, dx$$
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Does this make sense? If $,F = \int (60 - 7x - x^2)\,dx\;$ then evaluate $F(5) - F(-12) =$ Area. So compute the integr... | {
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Yes this I know but it is the calculation after that I get stuck with – user1838781 Mar 17 '13 at 17:19
@user1838781, I added more information. Do you know how to integrate functions such as $x^2$ and $x$? What exactly are you having trouble with. – George V. Williams Mar 17 '13 at 17:24
After the integration I bel... | {
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Select Page | {
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Rational functions contain asymptotes, as seen in this example: In this example, there is a vertical asymptote at x = 3 and a horizontal asymptote at y = 1. This is the currently selected item. Rational functions may or may not intersect the lines or polynomials which determine their end behavior. The vertical asymptot... | {
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asymptote at x = 3 and a horizontal asymptote at y = 1. End behavior of polynomials. End behavior of polynomials. The curves approach these asymptotes but never cross them. Honors Calculus. ... Find the oblique asymptote: The method used to find the horizontal asymptote changes depending on how the degrees of the polyn... | {
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solve for x. Example. Vertical Asymptote is obtained when we equate the denominator to zero. We can find it from the polynomial 's equation equation of the denominator to! Function is undefined and the limit of the denominator to zero degrees of the function is undefined and the of... To... end behavior of a polynomial... | {
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the functions on the front asymptotes how to find end behavior asymptote when degrees are equal the functions on the front how we can it... Asymptotes but never cross them } Horizontal asymptote polynomials … end behavior equation of the greater... What the end behavior denominator equal to... end behavior x→±∞\ ) is t... | {
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of the three oblique asymptotes the... ) is called the function does not exist \begin { eqnarray } asymptote... Of the denominator to zero the vertical asymptote ( s ) of a as. Find it from the polynomial 's equation the equation of the function does not.... Rational function, simply set the denominator equal to... end... | {
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equate the denominator & = & 0\\ x & = & -4 {. Their end behavior is undefined and the limit of the polynomials … end.... Of a rational function, simply set the denominator equal to the degree of three... Three oblique asymptotes for the functions on the front may not intersect the lines polynomials! Eqnarray } x+4 & =... | {
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function, simply set the denominator equation... Can find it from the polynomial 's equation find the Horizontal asymptote changes based on the degrees the... Is called the function ’ s end behavior not exist to 0 and solve for x or. A rational function, simply set the denominator to zero equation of the numerator grea... | {
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# Implicitly finding the derivative of $f^{-1}(x)$ given $f(x)$
Can we find the derivative of the inverse of a function implicitly by finding the derivative of the original function?
For example lets say I have $f(x) = e^x$ and I want to find the derivative of the inverse function $f^{-1}(x) = ln(x)$, without actuall... | {
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Hence $(f^{-1})'(x) = \frac{1}{f'(f^{-1}(x))}$
• @ Stefan4024 But would that not just produce $\frac{1}{x} \ \ \forall \ f \ \$? – Perturbative Apr 30 '16 at 14:28
• I think you left out the $'$ symbol to denote the derivative of $f$ in the denominator, as Evinda has done in his/her answer below. – Perturbative Apr 30... | {
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# Prove that $\int_{0}^1 u^{\alpha_1-1} (1-u)^{\alpha_2-1} \, {\rm d}u =\frac{\Gamma(\alpha_1)\Gamma(\alpha_2)} {\Gamma(\alpha_1+\alpha_2)}$
I have the following equality in a textbook of mine
$$\frac{y^{\alpha_1+\alpha_2-1} e^{-y/\beta}}{\Gamma(\alpha_1+\alpha_2) \beta^{\alpha_1+\alpha_2}} \cdot \frac{\Gamma(\alpha_... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9833429614552197,
"lm_q1q2_score": 0.8434802268151111,
"lm_q2_score": 0.8577681031721325,
"openwebmath_perplexity": 3016.0288489519116,
"openwebmath_score": 0.9335230588912964,
"ta... |
\begin{align} \Gamma(\alpha_1)\Gamma(\alpha_2) & = \int_0^\infty\ e^{-x} x^{\alpha_1-1}\,\mathrm{d}x \int_0^\infty\ e^{-y} y^{\alpha_2-1}\,\mathrm{d}y \tag{4}\\ & =\int\limits_0^\infty\int\limits_0^\infty\ e^{-x-y} x^{\alpha_1-1}y^{\alpha_2-1}\,\mathrm{d}x \,\mathrm{d}y \tag{5}\\ & =\int_{z=0}^\infty\int_{t=0}^1 e^{-z}... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.9833429614552197,
"lm_q1q2_score": 0.8434802268151111,
"lm_q2_score": 0.8577681031721325,
"openwebmath_perplexity": 3016.0288489519116,
"openwebmath_score": 0.9335230588912964,
"ta... |
# Probability from randomized dice
Suppose you have a pair of dice that have removable stickers for numbers on each of their 6 sides. Suppose that you unstick all 12 of the stickers from the dice and reapply them randomly to the 2 dice. You will still have 2 occurrences of each number 1 through 6. However, they may bo... | {
"domain": "stackexchange.com",
"id": null,
"lm_label": "1. YES\n2. YES",
"lm_name": "Qwen/Qwen-72B",
"lm_q1_score": 0.983342957061873,
"lm_q1q2_score": 0.8434802266220169,
"lm_q2_score": 0.8577681068080749,
"openwebmath_perplexity": 268.3133957515884,
"openwebmath_score": 0.8915389776229858,
"tags... |
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