Question

Why does the outer function $f$ of $f(g(x))$ have to be continuous?

score 184 · Answer 1 · 2026-03-25 04:25:15

184

Views

Why does the outer function $f$ of $f(g(x))$ have to be continuous?

Published on 25 Mar 2026 - 4:25

score 114 · Answer 2 · 2026-03-24 20:38:04

114

Views

Limit of $n$th root of exponentials

Published on 24 Mar 2026 - 20:38

score 100 · Answer 3 · 2026-04-10 17:47:19

100

Views

Evaluation of limits using McLaurin series

Published on 10 Apr 2026 - 17:47

score 11.8k · Answer 4 · 2018-01-24 17:24:27

11.8k

Views

If the limit of a sequence equals infinity as $n$ approaches infinity does the sequence diverge?

Published on 24 Jan 2018 - 17:24

score 99 · Answer 5 · 2026-04-10 15:42:29

99

Views

Show that $\lim_{(h,k)\rightarrow (0,0)}\frac{(2k+h)^2}{\sqrt{h^2+k^2}}=0.$

Published on 10 Apr 2026 - 15:42

score 75 · Answer 6 · 2026-04-01 10:09:31

75

Views

Limit when $x$ converges to $0$

Published on 01 Apr 2026 - 10:09

score 592 · Answer 7 · 2026-04-10 17:40:54

592

Views

When does $ |{x}|^\alpha\sin{\frac1{x}} $ have continuous derivative at zero?

Published on 10 Apr 2026 - 17:40

score 73 · Answer 8 · 2026-03-25 06:24:52

73

Views

Finding a limit including an improper integral: $\lim_{n\to\infty}⁡ \int_0^{\sqrt n} \left({1-\frac{x^2}{n}}\right)^n\,dx$

Published on 25 Mar 2026 - 6:24

score 68 · Answer 9 · 2026-04-10 17:06:30

68

Views

Limit where ${x\to 0}$

Published on 10 Apr 2026 - 17:06

score 55 · Answer 10 · 2018-01-24 22:55:52

55

Views

How to solve $\lim\limits_{x \to -\infty } e^{x^2/(1+x)}$?

Published on 24 Jan 2018 - 22:55

score 73 · Answer 11 · 2018-01-24 23:12:11

73

Views

How to solve $\lim_{x\to \infty}\bigg( 2^{\frac{1}{x}} - 2^{\frac{x-1}{x+1}}\bigg)$??

Published on 24 Jan 2018 - 23:12

score 123 · Answer 12 · 2026-04-09 02:55:14

123

Views

Limits of power of fractions

Published on 09 Apr 2026 - 2:55

score 194 · Answer 13 · 2026-04-07 22:37:22

194

Views

Trying to understand the usefulness of the delta-epsilon definitions of limits

Published on 07 Apr 2026 - 22:37

score 606 · Answer 14 · 2026-04-09 00:54:33

606

Views

Is function is uniformly continuous on $\mathbb{R}$ then it is uniformly continuous on subset of $\mathbb{R}$?

Published on 09 Apr 2026 - 0:54

score 666 · Answer 15 · 2018-01-25 05:52:46

666

Views

How to prove $\lim \limits_{x \to 1^-} \sum\limits_{n=0}^\infty (-1)^nx^{n^2} = \frac{1}{2} \ $?

Published on 25 Jan 2018 - 5:52

List Question

Why does the outer function $f$ of $f(g(x))$ have to be continuous?

Limit of $n$th root of exponentials

Evaluation of limits using McLaurin series

If the limit of a sequence equals infinity as $n$ approaches infinity does the sequence diverge?

Show that $\lim_{(h,k)\rightarrow (0,0)}\frac{(2k+h)^2}{\sqrt{h^2+k^2}}=0.$

Limit when $x$ converges to $0$

When does $ |{x}|^\alpha\sin{\frac1{x}} $ have continuous derivative at zero?

Finding a limit including an improper integral: $\lim_{n\to\infty}⁡ \int_0^{\sqrt n} \left({1-\frac{x^2}{n}}\right)^n\,dx$

Limit where ${x\to 0}$

How to solve $\lim\limits_{x \to -\infty } e^{x^2/(1+x)}$?

How to solve $\lim_{x\to \infty}\bigg( 2^{\frac{1}{x}} - 2^{\frac{x-1}{x+1}}\bigg)$??

Limits of power of fractions

Trying to understand the usefulness of the delta-epsilon definitions of limits

Is function is uniformly continuous on $\mathbb{R}$ then it is uniformly continuous on subset of $\mathbb{R}$?

How to prove $\lim \limits_{x \to 1^-} \sum\limits_{n=0}^\infty (-1)^nx^{n^2} = \frac{1}{2} \ $?

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