Question

How to prove that if $\lim(a_n)=a$ then $\lim(\frac{1}{a_n})=\frac{1}{a}$?

score 1.2k · Answer 1 · 2026-03-25 22:05:43

1.2k

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How to prove that if $\lim(a_n)=a$ then $\lim(\frac{1}{a_n})=\frac{1}{a}$?

Published on 25 Mar 2026 - 22:05

score 875 · Answer 2 · 2026-04-09 04:12:43

875

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Using Laplace transforms to evaluate$\int_{0}^{\infty}\frac{\sin^2(x)}{x^2(x^2 + 1)} dx$

Published on 09 Apr 2026 - 4:12

score 64 · Answer 3 · 2026-03-26 14:21:07

64

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The set of sequences of $\Bbb N$ and $\mathcal{P} (\Bbb N)$ are equinumerous.

Published on 26 Mar 2026 - 14:21

score 83 · Answer 4 · 2018-10-11 03:04:59

83

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Prove by contradiction $[(A\cap B)−(B\cap C)]−(A\cap C)'=\phi$.

Published on 11 Oct 2018 - 3:04

score 99 · Answer 5 · 2018-10-11 05:13:01

99

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Define an injection from $2^{\Bbb N}$ to $\Bbb R$

Published on 11 Oct 2018 - 5:13

score 1.5k · Answer 6 · 2018-10-11 10:56:24

1.5k

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Solving $y''+2y'+2y=e^{-x}\sin(x)$ using undetermined coefficients.

Published on 11 Oct 2018 - 10:56

score 1.2k · Answer 7 · 2026-03-25 22:05:21

1.2k

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Prove $F_{n+1} ≤ (\frac74)^n $, where $F_n$ are Fibonacci numbers

Published on 25 Mar 2026 - 22:05

score 495 · Answer 8 · 2018-10-11 11:12:17

495

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Closure of $\{1,\frac{1}{2},\frac{1}{3},\frac{1}{4},...\frac{1}{n},...\}$

Published on 11 Oct 2018 - 11:12

score 144 · Answer 9 · 2018-10-11 14:10:38

144

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Let $\tau$ denote the product topology on $X=X_1 \times X_2$. Then $(X,\tau)$ is a separable space.

Published on 11 Oct 2018 - 14:10

score 140 · Answer 10 · 2026-03-25 19:51:36

140

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Validity of allowing $\epsilon$ to vanish in Baby Rudin Theorem 3.10a

Published on 25 Mar 2026 - 19:51

score 344 · Answer 11 · 2026-03-26 14:21:16

344

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Let $X,Y,Z$ be nonempty sets. Then $|(X^Y)^Z|=|X^{Y\times Z}|$

Published on 26 Mar 2026 - 14:21

score 2.4k · Answer 12 · 2018-10-11 15:51:02

2.4k

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If $f:[0,1] \rightarrow \mathbb{R}$ is continuous function such that $f(0)=f(1)$ then there exists $ x\in [0,1]$ such that $f(x) = f(x+\frac{1}{n})$.

Published on 11 Oct 2018 - 15:51

score 287 · Answer 13 · 2026-04-11 22:19:38

287

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Proof of the chainrule: is this proof correct and did I use the right notation?

Published on 11 Apr 2026 - 22:19

score 712 · Answer 14 · 2018-10-11 20:07:22

712

Views

Proving continuity of Logarithm using $\delta$-$\epsilon$

Published on 11 Oct 2018 - 20:07

score 467 · Answer 15 · 2026-03-25 06:13:13

467

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Find the irreducible components of $V(x - yz, xz - y^2)$.

Published on 25 Mar 2026 - 6:13

List Question

How to prove that if $\lim(a_n)=a$ then $\lim(\frac{1}{a_n})=\frac{1}{a}$?

Using Laplace transforms to evaluate$\int_{0}^{\infty}\frac{\sin^2(x)}{x^2(x^2 + 1)} dx$

The set of sequences of $\Bbb N$ and $\mathcal{P} (\Bbb N)$ are equinumerous.

Prove by contradiction $[(A\cap B)−(B\cap C)]−(A\cap C)'=\phi$.

Define an injection from $2^{\Bbb N}$ to $\Bbb R$

Solving $y''+2y'+2y=e^{-x}\sin(x)$ using undetermined coefficients.

Prove $F_{n+1} ≤ (\frac74)^n $, where $F_n$ are Fibonacci numbers

Closure of $\{1,\frac{1}{2},\frac{1}{3},\frac{1}{4},...\frac{1}{n},...\}$

Let $\tau$ denote the product topology on $X=X_1 \times X_2$. Then $(X,\tau)$ is a separable space.

Validity of allowing $\epsilon$ to vanish in Baby Rudin Theorem 3.10a

Let $X,Y,Z$ be nonempty sets. Then $|(X^Y)^Z|=|X^{Y\times Z}|$

If $f:[0,1] \rightarrow \mathbb{R}$ is continuous function such that $f(0)=f(1)$ then there exists $ x\in [0,1]$ such that $f(x) = f(x+\frac{1}{n})$.

Proof of the chainrule: is this proof correct and did I use the right notation?

Proving continuity of Logarithm using $\delta$-$\epsilon$

Find the irreducible components of $V(x - yz, xz - y^2)$.

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