Question

Prove that if $\lim_{x\rightarrow c}f(x)=L$ and $\lim_{x\rightarrow c}g(x)=M$ then $\lim_{x\rightarrow c}f(x)g(x)=LM$.

score 305 · Answer 1 · 2018-04-04 05:11:15

305

Views

Prove that if $\lim_{x\rightarrow c}f(x)=L$ and $\lim_{x\rightarrow c}g(x)=M$ then $\lim_{x\rightarrow c}f(x)g(x)=LM$.

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score 80 · Answer 2 · 2026-03-25 12:01:17

80

Views

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score 659 · Answer 3 · 2026-03-25 13:48:40

659

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score 114 · Answer 4 · 2026-03-25 11:08:28

114

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score 56 · Answer 5 · 2018-04-05 19:55:27

56

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Show that for every vector $c \in \Bbb{R}^n$, the vector $A^T(AA^T)^{-1}Ac$ is orthogonal to the null space of the matrix $A$.

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1.1k

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score 54 · Answer 8 · 2018-04-08 15:25:49

54

Views

Proof explanation: Let $\mathsf{V,W}$ are vector spaces, $u\in\mathsf{V}$, then $[\mathsf{T}(u)]_\gamma=[\mathsf{T}]_\beta^\gamma[u]_\beta$

Published on 08 Apr 2018 - 15:25

score 533 · Answer 9 · 2018-04-09 15:09:42

533

Views

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score 390 · Answer 10 · 2026-03-25 06:03:36

390

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score 643 · Answer 11 · 2018-04-11 18:27:28

643

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If $f(xy)=xf(y)$ for all $x,y\in \mathbb{R}$, then $f(x+y)=f(x)+f(y)$

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score 144 · Answer 12 · 2018-04-13 13:32:13

144

Views

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score 60 · Answer 13 · 2018-04-14 18:18:11

60

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score 18 · Answer 14 · 2026-03-23 09:46:21

18

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score 39 · Answer 15 · 2026-03-25 17:42:21

39

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List Question

Prove that if $\lim_{x\rightarrow c}f(x)=L$ and $\lim_{x\rightarrow c}g(x)=M$ then $\lim_{x\rightarrow c}f(x)g(x)=LM$.

sum of piece wise is piece wise

On the asymptotic behavior of the Fourier coefficients of $(1-R\cos\theta)^{-3/2}$

Lambda-Calculus - Alternative proof without fixed point combinator

Show that for every vector $c \in \Bbb{R}^n$, the vector $A^T(AA^T)^{-1}Ac$ is orthogonal to the null space of the matrix $A$.

Algebraic closure of $\mathbb{Q}$ in $\mathbb{C}$. Alternative proof?

Lambda Calculus - Exercise with fixed point combinator

Proof explanation: Let $\mathsf{V,W}$ are vector spaces, $u\in\mathsf{V}$, then $[\mathsf{T}(u)]_\gamma=[\mathsf{T}]_\beta^\gamma[u]_\beta$

Why is it obvious that if the intersection of all sets is empty then its complements cover the whole space?

Showing the kernel of a set $X\subset \Bbb R^2$ is convex

If $f(xy)=xf(y)$ for all $x,y\in \mathbb{R}$, then $f(x+y)=f(x)+f(y)$

Riemann $\zeta$-function and a series involving Stirling numbers of first kind.

Finding the function for a given power series in $\mathbb{C}$

Question regarding maximum of a set

Alternative proof to the proposition that surjectivity of $f:X\to Y$ implies $|X|\ge|Y|$

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