Question

Given $\phi (u)=\sin u, u\in E$, and $f(t)=(t^2,\sqrt{t})$, find an interval $E$ such that $f\circ \phi$ is defined and differentiable on $E$

score 22 · Answer 1 · 2019-03-05 23:36:13

Given $\phi (u)=\sin u, u\in E$, and $f(t)=(t^2,\sqrt{t})$, find an interval $E$ such that $f\circ \phi$ is defined and differentiable on $E$

score 23 · Answer 2 · 2019-03-06 18:08:56

23

Views

Calculate the length of the following smooth simple arcs in $\mathbb{R}^2$.

Published on 06 Mar 2019 - 18:08

score 39 · Answer 3 · 2026-03-26 23:10:49

39

Views

Find the tangent line at pont $q=(a,b)$ of the following curves.

Published on 26 Mar 2026 - 23:10

score 91 · Answer 4 · 2019-03-06 22:39:20

91

Views

How to calculate $\int_{0}^{4} \sqrt{\frac{t+4}{t}}dt$?

Published on 06 Mar 2019 - 22:39

score 408 · Answer 5 · 2019-03-07 13:18:39

408

Views

How to think of gradient of a vector?

Published on 07 Mar 2019 - 13:18

score 22 · Answer 6 · 2026-03-29 14:55:53

22

Views

$L_1$ distance between re-normalized points

Published on 29 Mar 2026 - 14:55

score 53 · Answer 7 · 2019-03-08 06:17:41

53

Views

Show that the curvature of simple arc C is given by $\kappa(q)=\frac{\Vert f'(a)\times f''(a)\Vert}{\Vert f''(a)\Vert^3}$

Published on 08 Mar 2019 - 6:17

score 173 · Answer 8 · 2019-03-08 12:03:19

173

Views

Does the following mean value theorem type statement hold in $\mathbb{R}^{n}$

Published on 08 Mar 2019 - 12:03

score 21 · Answer 9 · 2019-03-08 18:54:46

21

Views

Notations in the proof that $\forall x \in \mathbb{R}^d f(x+h) = f(x) + \langle\nabla f(x), h\rangle + o(\|\textbf{h}\|)$

Published on 08 Mar 2019 - 18:54

score 39 · Answer 10 · 2019-03-08 22:28:08

39

Views

How do I prove the fact that any vector in $n$ dimensions can be written as a linear combination of $n$ separate vectors?

Published on 08 Mar 2019 - 22:28

score 44 · Answer 11 · 2019-03-08 22:39:03

Find the unit tangent, the principal normal and the curvature of $\frac{x^2}{9}+\frac{y^2}{4}=1$ at $(\frac{-3}{\sqrt{2}},\frac{2}{\sqrt{2}})\in C$

score 3.3k · Answer 12 · 2019-03-09 05:59:18

3.3k

Views

Prove that if a particle moves in constant speed, its acceleration is orthogonal to its velocity.

Published on 09 Mar 2019 - 5:59

score 6.3k · Answer 13 · 2019-03-09 16:06:12

6.3k

Views

Radial and transverse components of velocity and acceleration.

Published on 09 Mar 2019 - 16:06

score 59 · Answer 14 · 2026-03-28 16:13:36

59

Views

Limits of two sequences of vectors being parallel?

Published on 28 Mar 2026 - 16:13

score 16.6k · Answer 15 · 2026-03-26 04:30:37

16.6k

Views

Divergence of a vector field in cylindrical coordinates

Published on 26 Mar 2026 - 4:30

List Question

Given $\phi (u)=\sin u, u\in E$, and $f(t)=(t^2,\sqrt{t})$, find an interval $E$ such that $f\circ \phi$ is defined and differentiable on $E$

Calculate the length of the following smooth simple arcs in $\mathbb{R}^2$.

Find the tangent line at pont $q=(a,b)$ of the following curves.

How to calculate $\int_{0}^{4} \sqrt{\frac{t+4}{t}}dt$?

How to think of gradient of a vector?

$L_1$ distance between re-normalized points

Show that the curvature of simple arc C is given by $\kappa(q)=\frac{\Vert f'(a)\times f''(a)\Vert}{\Vert f''(a)\Vert^3}$

Does the following mean value theorem type statement hold in $\mathbb{R}^{n}$

Notations in the proof that $\forall x \in \mathbb{R}^d f(x+h) = f(x) + \langle\nabla f(x), h\rangle + o(\|\textbf{h}\|)$

How do I prove the fact that any vector in $n$ dimensions can be written as a linear combination of $n$ separate vectors?

Find the unit tangent, the principal normal and the curvature of $\frac{x^2}{9}+\frac{y^2}{4}=1$ at $(\frac{-3}{\sqrt{2}},\frac{2}{\sqrt{2}})\in C$

Prove that if a particle moves in constant speed, its acceleration is orthogonal to its velocity.

Radial and transverse components of velocity and acceleration.

Limits of two sequences of vectors being parallel?

Divergence of a vector field in cylindrical coordinates

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