Question

If $f(x) \le M$ and $\lim_{x \to a} f(x) = A$, prove that $A \le M$.

score 96 · Answer 1 · 2026-04-17 22:19:43

96

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If $f(x) \le M$ and $\lim_{x \to a} f(x) = A$, prove that $A \le M$.

Published on 17 Apr 2026 - 22:19

score 85 · Answer 2 · 2026-05-05 06:55:00

85

Views

$\lim_{n \to \infty}\sum_{r=1}^{n}\frac{r^2}{n^3 + n^2 + r}$

Published on 05 May 2026 - 6:55

score 152 · Answer 3 · 2026-04-17 12:18:56

152

Views

Evaluate $\int_1^{\infty} \frac {(\{x\}-\frac 12)dx}{x}$

Published on 17 Apr 2026 - 12:18

score 75 · Answer 4 · 2026-04-23 18:28:11

75

Views

Limits , indeterminate form

Published on 23 Apr 2026 - 18:28

score 92 · Answer 5 · 2026-04-11 16:03:20

92

Views

Order of Integration in Divergent Integrals

Published on 11 Apr 2026 - 16:03

score 36 · Answer 6 · 2026-04-12 00:28:50

36

Views

Trouble with L'Hôpital Justification for Complicated Limit of Integral

Published on 12 Apr 2026 - 0:28

score 183 · Answer 7 · 2026-04-16 15:40:33

183

Views

Evaluate $\lim_{n \to \infty} \sqrt{n^2+2n}-\left[\sqrt{n^2+2n}\right]$

Published on 16 Apr 2026 - 15:40

score 55 · Answer 8 · 2026-04-17 13:44:37

Does $\lim_{x\to\infty}\frac{f(x)+g(x)}{p(x)+q(x)}$ exist if $\lim_{x\to\infty}\left[\frac{f(x)}{p(x)}+\frac{g(x)}{q(x)}\right]$ exists?

score 55 · Answer 9 · 2026-04-16 07:02:17

55

Views

If $\lim_{x\to a}f(x)=\infty$ and $\lim_{x\to a}g(x)=\infty$ then $\lim_{x\to a}\frac{f(x)}{g(x)}=1\iff\lim_{x\to a}(f(x)-g(x))=0$

Published on 16 Apr 2026 - 7:02

score 49 · Answer 10 · 2026-04-28 12:15:09

49

Views

Differentiability and tangent relationship

Published on 28 Apr 2026 - 12:15

score 1k · Answer 11 · 2026-04-17 03:48:04

1k

Views

Evaluate $\lim_{x\to \infty}\frac{x^{2018}+2017^x}{x^{2017}+2018^x}$

Published on 17 Apr 2026 - 3:48

score 90 · Answer 12 · 2026-04-17 14:21:21

90

Views

Approximations to Radial Stress in a Spherical Shell

Published on 17 Apr 2026 - 14:21

score 44 · Answer 13 · 2026-04-25 21:06:41

44

Views

Multiple Variable Limits

Published on 25 Apr 2026 - 21:06

score 121 · Answer 14 · 2026-04-16 08:32:14

121

Views

Find multivariable limit $\lim_{(x,y)\to(0,0)}\frac{x^2y^2}{\sqrt{x^2y^2+(x-y)^2}}$

Published on 16 Apr 2026 - 8:32

score 137 · Answer 15 · 2026-04-16 05:34:58

137

Views

Prove that $\displaystyle \lim_{n\to \infty} a_n\le\lim_{n\to \infty}b_n$

Published on 16 Apr 2026 - 5:34

List Question

If $f(x) \le M$ and $\lim_{x \to a} f(x) = A$, prove that $A \le M$.

$\lim_{n \to \infty}\sum_{r=1}^{n}\frac{r^2}{n^3 + n^2 + r}$

Evaluate $\int_1^{\infty} \frac {(\{x\}-\frac 12)dx}{x}$

Limits , indeterminate form

Order of Integration in Divergent Integrals

Trouble with L'Hôpital Justification for Complicated Limit of Integral

Evaluate $\lim_{n \to \infty} \sqrt{n^2+2n}-\left[\sqrt{n^2+2n}\right]$

Does $\lim_{x\to\infty}\frac{f(x)+g(x)}{p(x)+q(x)}$ exist if $\lim_{x\to\infty}\left[\frac{f(x)}{p(x)}+\frac{g(x)}{q(x)}\right]$ exists?

If $\lim_{x\to a}f(x)=\infty$ and $\lim_{x\to a}g(x)=\infty$ then $\lim_{x\to a}\frac{f(x)}{g(x)}=1\iff\lim_{x\to a}(f(x)-g(x))=0$

Differentiability and tangent relationship

Evaluate $\lim_{x\to \infty}\frac{x^{2018}+2017^x}{x^{2017}+2018^x}$

Approximations to Radial Stress in a Spherical Shell

Multiple Variable Limits

Find multivariable limit $\lim_{(x,y)\to(0,0)}\frac{x^2y^2}{\sqrt{x^2y^2+(x-y)^2}}$

Prove that $\displaystyle \lim_{n\to \infty} a_n\le\lim_{n\to \infty}b_n$

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