Question

If $f$ is two times differentiable on $[a,b]$ and attains maximum at $x_0\in (a,b)$, prove $f''(x_0)\leq 0$.

score 152 · Answer 1 · 2026-04-28 15:09:38

152

Views

If $f$ is two times differentiable on $[a,b]$ and attains maximum at $x_0\in (a,b)$, prove $f''(x_0)\leq 0$.

Published on 28 Apr 2026 - 15:09

score 305 · Answer 2 · 2026-04-15 17:48:32

305

Views

Evaluate $\sum_{r=1}^{\infty} \sqrt {\frac {r}{r^4+r^2+1}}$

Published on 15 Apr 2026 - 17:48

score 144 · Answer 3 · 2026-04-23 06:18:13

144

Views

Find limit distribution of given random variable

Published on 23 Apr 2026 - 6:18

score 120 · Answer 4 · 2026-04-15 11:17:12

120

Views

Find all values of $a$ for which $\lim_{x\to 1}h(x)$ exists

Published on 15 Apr 2026 - 11:17

score 46 · Answer 5 · 2026-04-15 07:06:37

46

Views

Limit of this sequence

Published on 15 Apr 2026 - 7:06

score 101 · Answer 6 · 2026-04-28 16:34:05

101

Views

Why is $\lim_{x\to a}{[f(x)\cdot g(x)]}=\lim_{x\to a}{f(x)}\cdot\lim_{x\to a}{g(x)}$, but $(fg)' = f'g+fg'$

Published on 28 Apr 2026 - 16:34

score 151 · Answer 7 · 2026-04-14 12:50:38

151

Views

Does a converging sequence of measurable functions necessarily converge towards a measurable function?

Published on 14 Apr 2026 - 12:50

score 155 · Answer 8 · 2026-04-14 17:41:37

155

Views

How do I find $\lim_{(x,y) \to (0,0)} \frac{\sqrt{xy + 1} -1}{x + y}$?

Published on 14 Apr 2026 - 17:41

score 40 · Answer 9 · 2026-04-14 01:32:09

40

Views

Proving $\prod_{k=1}^n (1+c_{k,n}) \to e^\lambda$ as $n\to \infty$ under certain assumptions

Published on 14 Apr 2026 - 1:32

score 49 · Answer 10 · 2026-04-12 15:51:57

49

Views

Does limit of "approximate zero set" converge to the zero set?

Published on 12 Apr 2026 - 15:51

score 164 · Answer 11 · 2026-04-26 00:22:24

164

Views

Directional Derivatives - Multivariable Calculus

Published on 26 Apr 2026 - 0:22

score 84 · Answer 12 · 2026-04-14 22:46:30

84

Views

Finding $\lim_{n\rightarrow \infty}\frac{1}{n^2}\sum^{n}_{r=0}\ln\binom{n}{r}$.

Published on 14 Apr 2026 - 22:46

score 48 · Answer 13 · 2026-04-16 00:36:38

48

Views

Calculate $\lim_{x \longrightarrow 0^{-}}(1-2^x)^{\sin(x)}$ by Taylor expansion.

Published on 16 Apr 2026 - 0:36

score 61 · Answer 14 · 2026-04-14 22:40:07

61

Views

Indeterminate forms - zero × inf determinate?

Published on 14 Apr 2026 - 22:40

score 619 · Answer 15 · 2026-04-16 12:28:47

619

Views

Convergence of a recursive sequence $u_n$

Published on 16 Apr 2026 - 12:28

List Question

If $f$ is two times differentiable on $[a,b]$ and attains maximum at $x_0\in (a,b)$, prove $f''(x_0)\leq 0$.

Evaluate $\sum_{r=1}^{\infty} \sqrt {\frac {r}{r^4+r^2+1}}$

Find limit distribution of given random variable

Find all values of $a$ for which $\lim_{x\to 1}h(x)$ exists

Limit of this sequence

Why is $\lim_{x\to a}{[f(x)\cdot g(x)]}=\lim_{x\to a}{f(x)}\cdot\lim_{x\to a}{g(x)}$, but $(fg)' = f'g+fg'$

Does a converging sequence of measurable functions necessarily converge towards a measurable function?

How do I find $\lim_{(x,y) \to (0,0)} \frac{\sqrt{xy + 1} -1}{x + y}$?

Proving $\prod_{k=1}^n (1+c_{k,n}) \to e^\lambda$ as $n\to \infty$ under certain assumptions

Does limit of "approximate zero set" converge to the zero set?

Directional Derivatives - Multivariable Calculus

Finding $\lim_{n\rightarrow \infty}\frac{1}{n^2}\sum^{n}_{r=0}\ln\binom{n}{r}$.

Calculate $\lim_{x \longrightarrow 0^{-}}(1-2^x)^{\sin(x)}$ by Taylor expansion.

Indeterminate forms - zero × inf determinate?

Convergence of a recursive sequence $u_n$

Trending Questions

Popular # Hahtags

Popular Questions