Question

Is this the right way to prove basic limit identities?

score 108 · Answer 1 · 2026-04-13 23:28:16

108

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Is this the right way to prove basic limit identities?

Published on 13 Apr 2026 - 23:28

score 1.8k · Answer 2 · 2026-04-13 22:36:49

1.8k

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Let f be a continuous and differentiable function such that f(a)=f(b)=0

Published on 13 Apr 2026 - 22:36

score 157 · Answer 3 · 2026-04-14 05:40:31

157

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Computing $\lim\limits_{n\to \infty} \frac{\ln^2n}{n}\sum\limits_{k=2}^{n-2}\frac{1}{\ln k\ln(n-k)}$

Published on 14 Apr 2026 - 5:40

score 6.2k · Answer 4 · 2026-04-11 13:09:37

6.2k

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Why are we allowed to cancel fractions in limits?

Published on 11 Apr 2026 - 13:09

score 32 · Answer 5 · 2026-04-14 23:52:46

32

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Relation between difference of values of an increasing function and difference of its arguments

Published on 14 Apr 2026 - 23:52

score 52 · Answer 6 · 2026-04-15 11:20:36

52

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If $\sin (y)=x\sin (a+y)$, prove that:

Published on 15 Apr 2026 - 11:20

score 478 · Answer 7 · 2026-04-09 22:30:21

478

Views

Finding the derivative of a function using its series expansion

Published on 09 Apr 2026 - 22:30

score 28 · Answer 8 · 2026-04-17 01:35:32

28

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Slopes and tangent lines

Published on 17 Apr 2026 - 1:35

score 69 · Answer 9 · 2026-03-24 21:22:36

69

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Using partial derivatives to prove whether a function is differential at a point

Published on 24 Mar 2026 - 21:22

score 1.2k · Answer 10 · 2026-04-12 08:53:46

1.2k

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Can a subsequence repeat a term finitely many times?

Published on 12 Apr 2026 - 8:53

score 40 · Answer 11 · 2026-04-14 15:11:34

40

Views

Taking the derivative of a product, which is made up of two quotients

Published on 14 Apr 2026 - 15:11

score 667 · Answer 12 · 2026-04-15 04:41:39

667

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Is there an analytic way to solve $\lim_{x \to 0} \cos\left(\frac{1}{x}\right)$?

Published on 15 Apr 2026 - 4:41

score 116 · Answer 13 · 2026-04-17 15:41:32

116

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Integrate $\int \frac{x^2}{(x^2+2x+2) \sqrt{x-1}} dx$

Published on 17 Apr 2026 - 15:41

score 135 · Answer 14 · 2026-04-11 03:27:51

135

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Differentiability of a multivariable function with directional derivatives existing

Published on 11 Apr 2026 - 3:27

score 79 · Answer 15 · 2026-04-13 20:23:35

79

Views

Given a convergence series $\sum 3^na_n$. Prove/disprove: The series $\sum (-2)^na_n$ converges.

Published on 13 Apr 2026 - 20:23

List Question

Is this the right way to prove basic limit identities?

Let f be a continuous and differentiable function such that f(a)=f(b)=0

Computing $\lim\limits_{n\to \infty} \frac{\ln^2n}{n}\sum\limits_{k=2}^{n-2}\frac{1}{\ln k\ln(n-k)}$

Why are we allowed to cancel fractions in limits?

Relation between difference of values of an increasing function and difference of its arguments

If $\sin (y)=x\sin (a+y)$, prove that:

Finding the derivative of a function using its series expansion

Slopes and tangent lines

Using partial derivatives to prove whether a function is differential at a point

Can a subsequence repeat a term finitely many times?

Taking the derivative of a product, which is made up of two quotients

Is there an analytic way to solve $\lim_{x \to 0} \cos\left(\frac{1}{x}\right)$?

Integrate $\int \frac{x^2}{(x^2+2x+2) \sqrt{x-1}} dx$

Differentiability of a multivariable function with directional derivatives existing

Given a convergence series $\sum 3^na_n$. Prove/disprove: The series $\sum (-2)^na_n$ converges.

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