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 308 · Answer 1 · 2026-04-15 19:04:04

308

Views

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

Published on 15 Apr 2026 - 19:04

score 85 · Answer 2 · 2026-05-10 11:53:52

85

Views

sum of piece wise is piece wise

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score 666 · Answer 3 · 2026-05-10 11:42:49

666

Views

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

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score 118 · Answer 4 · 2026-05-10 14:45:41

118

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Lambda-Calculus - Alternative proof without fixed point combinator

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score 59 · Answer 5 · 2026-04-16 04:10:17

59

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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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score 1.1k · Answer 6 · 2026-04-15 18:49:28

1.1k

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

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score 225 · Answer 7 · 2026-05-10 14:45:42

225

Views

Lambda Calculus - Exercise with fixed point combinator

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score 57 · Answer 8 · 2026-04-16 10:41:38

57

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 16 Apr 2026 - 10:41

score 536 · Answer 9 · 2026-04-15 20:43:00

536

Views

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

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score 394 · Answer 10 · 2026-05-10 16:13:13

394

Views

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

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score 646 · Answer 11 · 2026-04-17 14:08:41

646

Views

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

Published on 17 Apr 2026 - 14:08

score 147 · Answer 12 · 2026-04-11 12:00:32

147

Views

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

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score 63 · Answer 13 · 2026-04-09 17:19:48

63

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Published on 09 Apr 2026 - 17:19

score 21 · Answer 14 · 2026-04-14 08:12:52

21

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score 41 · Answer 15 · 2026-04-12 05:23:53

41

Views

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

Published on 12 Apr 2026 - 5:23

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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