Question

An application of mean value theorem

score 310 · Answer 1 · 2026-04-09 04:15:42

310

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An application of mean value theorem

Published on 09 Apr 2026 - 4:15

score 187 · Answer 2 · 2026-04-17 05:44:33

187

Views

Taylor series of $\ln\frac{1+x}{1-x}$

Published on 17 Apr 2026 - 5:44

score 43 · Answer 3 · 2026-04-15 23:18:15

43

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If $f>0$ and $(\ln f)'=f'/f$ is Lipschitz continuous, are we able to conclude that $(\ln f)'''$ is bounded?

Published on 15 Apr 2026 - 23:18

score 1.2k · Answer 4 · 2026-04-15 22:37:55

1.2k

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Find the value of $\frac{df^{-1}}{dx}$ of the following function

Published on 15 Apr 2026 - 22:37

score 98 · Answer 5 · 2026-05-10 15:52:34

98

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If $f$ is analytic on $(a, b)$ containing at point $x_{0}$ with $f^{(n)}(x_{0}) = 0$ for $n \in \mathbb{N}$, prove $f(x) = 0$ for all $x$.

Published on 10 May 2026 - 15:52

score 130 · Answer 6 · 2026-04-17 00:05:29

Let $f(x)=\cos \left[\cot ^{-1}\left( \frac{\cos x}{\sqrt{1-\cos 2x}}\right)\right]$ where $\frac{\pi}4<x<\frac{\pi}2$. Find $\frac{df(x)}{d\cot(x)}$

score 60 · Answer 7 · 2026-04-12 18:58:22

60

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Finding an example of a function $f(x)$ that is differentiable on $(a,b)$ but $f'(x)$ is not continuous on $(a,b)$.

Published on 12 Apr 2026 - 18:58

score 58 · Answer 8 · 2026-04-17 07:45:20

58

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Prove that the function $f(x) = \sum_{k =1}^{\infty} \frac{\sin(kx)}{2^{k}}$ is infinitely differentiable

Published on 17 Apr 2026 - 7:45

score 197 · Answer 9 · 2026-04-14 13:25:38

197

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Suppose that $f_k$ is a sequence of differentiable functions that converges uniformly to a function $f$. Must $f$ be differentiable?

Published on 14 Apr 2026 - 13:25

score 212 · Answer 10 · 2026-05-10 22:05:14

212

Views

Stuck on proof using Cauchy's integral formula

Published on 10 May 2026 - 22:05

score 530 · Answer 11 · 2026-04-16 10:10:14

530

Views

Let $f (z) = u+iv$ be an analytic function, then show that $ (∂^2/∂x^2 + ∂^2/∂y^2)|f(z)|^2 = 4|f'(z)|^2 $.

Published on 16 Apr 2026 - 10:10

score 40 · Answer 12 · 2026-04-14 03:35:20

40

Views

Partial Differential

Published on 14 Apr 2026 - 3:35

score 65 · Answer 13 · 2026-04-11 19:35:05

65

Views

Chain rule doubt

Published on 11 Apr 2026 - 19:35

score 252 · Answer 14 · 2026-04-09 13:20:39

252

Views

Computation of partial fraction decomposition

Published on 09 Apr 2026 - 13:20

score 440 · Answer 15 · 2026-05-10 14:58:57

440

Views

Derivative of nonsmooth functions

Published on 10 May 2026 - 14:58

List Question

An application of mean value theorem

Taylor series of $\ln\frac{1+x}{1-x}$

If $f>0$ and $(\ln f)'=f'/f$ is Lipschitz continuous, are we able to conclude that $(\ln f)'''$ is bounded?

Find the value of $\frac{df^{-1}}{dx}$ of the following function

If $f$ is analytic on $(a, b)$ containing at point $x_{0}$ with $f^{(n)}(x_{0}) = 0$ for $n \in \mathbb{N}$, prove $f(x) = 0$ for all $x$.

Let $f(x)=\cos \left[\cot ^{-1}\left( \frac{\cos x}{\sqrt{1-\cos 2x}}\right)\right]$ where $\frac{\pi}4<x<\frac{\pi}2$. Find $\frac{df(x)}{d\cot(x)}$

Finding an example of a function $f(x)$ that is differentiable on $(a,b)$ but $f'(x)$ is not continuous on $(a,b)$.

Prove that the function $f(x) = \sum_{k =1}^{\infty} \frac{\sin(kx)}{2^{k}}$ is infinitely differentiable

Suppose that $f_k$ is a sequence of differentiable functions that converges uniformly to a function $f$. Must $f$ be differentiable?

Stuck on proof using Cauchy's integral formula

Let $f (z) = u+iv$ be an analytic function, then show that $ (∂^2/∂x^2 + ∂^2/∂y^2)|f(z)|^2 = 4|f'(z)|^2 $.

Partial Differential

Chain rule doubt

Computation of partial fraction decomposition

Derivative of nonsmooth functions

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