Question

Find the linear taylor expansion for $f(x,y) = x\cos y + y\sin x$ and give a bound to the error

score 230 · Answer 1 · 2026-04-15 22:34:30

230

Views

Find the linear taylor expansion for $f(x,y) = x\cos y + y\sin x$ and give a bound to the error

Published on 15 Apr 2026 - 22:34

score 158 · Answer 2 · 2026-04-16 08:25:21

158

Views

If $f(x)$ is odd, then prove that $f'(0)=0$

Published on 16 Apr 2026 - 8:25

score 265 · Answer 3 · 2026-04-16 17:34:37

265

Views

The relation between Frechet derivative and differentiation in $\mathbb{R}^2$

Published on 16 Apr 2026 - 17:34

score 267 · Answer 4 · 2026-03-25 06:21:02

267

Views

James R. Munkres "Analysis on Manifolds" p.60 Theorem 7.4.

Published on 25 Mar 2026 - 6:21

score 38 · Answer 5 · 2026-04-28 08:26:09

38

Views

Let $f:E\to \Bbb{R},\;p\mapsto f(p)=\int_{0}^{1}p^3{(t)}dt$. Then $f$ is differentiable and we can compute $f'(u)$

Published on 28 Apr 2026 - 8:26

score 2.5k · Answer 6 · 2026-04-16 06:07:24

2.5k

Views

Find partial derivatives of $f(x,y)= \sqrt {xy}$ at the point $(0,0)$

Published on 16 Apr 2026 - 6:07

score 1.2k · Answer 7 · 2026-04-16 13:04:46

1.2k

Views

Find all $x$ values such that the tangent line to the given curve satisfy a specific property

Published on 16 Apr 2026 - 13:04

score 102 · Answer 8 · 2026-04-15 20:25:09

102

Views

Prove that $\Phi$ is differentiable on $E$ and find $\Phi'(x)$

Published on 15 Apr 2026 - 20:25

score 199 · Answer 9 · 2026-04-16 14:34:21

199

Views

Find the $n$-th derivative of $f(x)=\frac{x}{\sqrt{1-x}}$

Published on 16 Apr 2026 - 14:34

score 6.1k · Answer 10 · 2026-04-16 10:03:40

6.1k

Views

Find the gradient and hessian of $f(Ax+b)$ for real value $f$ and matrix $A$

Published on 16 Apr 2026 - 10:03

score 144 · Answer 11 · 2026-04-16 04:45:58

144

Views

Is $\limsup |C_n|^{\frac{1}{n}} = \limsup |C_{n+j}|^{\frac{1}{n}}? $ where $j\geq0 $

Published on 16 Apr 2026 - 4:45

score 71 · Answer 12 · 2026-04-17 10:33:18

71

Views

Solve the following problem, $u'(t)+p(t)u(t)=0,\;\;u(0)=0,$ $p(t)=\begin{cases}2& 0\leq t< 1,\\1 &t\geq 1\end{cases}.$

Published on 17 Apr 2026 - 10:33

score 61 · Answer 13 · 2026-04-15 16:43:26

61

Views

Laplace inverse of $(s+2)U(s)=0$ and $(s+1)U(s)=0.$

Published on 15 Apr 2026 - 16:43

score 106 · Answer 14 · 2026-04-13 03:03:10

106

Views

Strictly decreasing and concave down takes on negative values

Published on 13 Apr 2026 - 3:03

score 205 · Answer 15 · 2026-04-16 07:25:19

If $f: U \to \mathbb{R}^{n}$ is differentiable and $\Vert df(x) \Vert \leq K$ for any $x \in U$ then $\Vert f(x) - f(y) \Vert \leq Kd(x,y)$

List Question

Find the linear taylor expansion for $f(x,y) = x\cos y + y\sin x$ and give a bound to the error

If $f(x)$ is odd, then prove that $f'(0)=0$

The relation between Frechet derivative and differentiation in $\mathbb{R}^2$

James R. Munkres "Analysis on Manifolds" p.60 Theorem 7.4.

Let $f:E\to \Bbb{R},\;p\mapsto f(p)=\int_{0}^{1}p^3{(t)}dt$. Then $f$ is differentiable and we can compute $f'(u)$

Find partial derivatives of $f(x,y)= \sqrt {xy}$ at the point $(0,0)$

Find all $x$ values such that the tangent line to the given curve satisfy a specific property

Prove that $\Phi$ is differentiable on $E$ and find $\Phi'(x)$

Find the $n$-th derivative of $f(x)=\frac{x}{\sqrt{1-x}}$

Find the gradient and hessian of $f(Ax+b)$ for real value $f$ and matrix $A$

Is $\limsup |C_n|^{\frac{1}{n}} = \limsup |C_{n+j}|^{\frac{1}{n}}? $ where $j\geq0 $

Solve the following problem, $u'(t)+p(t)u(t)=0,\;\;u(0)=0,$ $p(t)=\begin{cases}2& 0\leq t< 1,\\1 &t\geq 1\end{cases}.$

Laplace inverse of $(s+2)U(s)=0$ and $(s+1)U(s)=0.$

Strictly decreasing and concave down takes on negative values

If $f: U \to \mathbb{R}^{n}$ is differentiable and $\Vert df(x) \Vert \leq K$ for any $x \in U$ then $\Vert f(x) - f(y) \Vert \leq Kd(x,y)$

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