Question

Prob. 4, Exercises 8.14, in Apostol's CALCULUS Vol II: Computing the gradient vector and a directional derivative for a scalar field

score 816 · Answer 1 · 2026-04-24 03:52:03

816

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Prob. 4, Exercises 8.14, in Apostol's CALCULUS Vol II: Computing the gradient vector and a directional derivative for a scalar field

Published on 24 Apr 2026 - 3:52

score 178 · Answer 2 · 2026-04-24 03:53:33

178

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Prob. 5, Exercises 8.14, in Apostol's CALCULUS Vol II: Find constants such that the directional derivative

Published on 24 Apr 2026 - 3:53

score 69 · Answer 3 · 2026-04-15 14:52:19

69

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Positive semi-definiteness of the Jacobian of the partial derivatives of distinct convex functions

Published on 15 Apr 2026 - 14:52

score 132 · Answer 4 · 2026-04-16 16:17:37

132

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Evaluate the Limit $\lim_{x \to 0}\frac{x}{\sqrt{1-e^{-x^2}}}$

Published on 16 Apr 2026 - 16:17

score 49 · Answer 5 · 2026-04-10 03:10:16

49

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Directional derivative.

Published on 10 Apr 2026 - 3:10

score 232 · Answer 6 · 2026-04-24 07:02:24

232

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Prob. 6, Exercises 8.14, in Apostol's CALCULUS Vol II: Given a scalar field differentiable at a point ...

Published on 24 Apr 2026 - 7:02

score 100 · Answer 7 · 2026-04-13 18:49:29

100

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Nonstandard-Analysis: Showing L'Hospital

Published on 13 Apr 2026 - 18:49

score 42 · Answer 8 · 2026-04-12 02:03:32

42

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Can limit be taken inside a function which has a removable Discontinuity

Published on 12 Apr 2026 - 2:03

score 531 · Answer 9 · 2026-04-24 05:19:07

531

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Can the gradient of a non-constant scalar field be zero?

Published on 24 Apr 2026 - 5:19

score 302 · Answer 10 · 2026-04-16 10:38:27

302

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Prob. 9, Exercises 8.14, in Apostol's CALCULUS Vol II: If the derivatives of a scalar field on an open ball vanish in $n$ independent directions,

Published on 16 Apr 2026 - 10:38

score 353 · Answer 11 · 2026-04-17 09:42:54

353

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Prob. 10, Exercises 8.14, in Apostol's CALCULUS Vol II: If the gradient of a differentiable scalar field is zero on an open ball, . . .

Published on 17 Apr 2026 - 9:42

score 911 · Answer 12 · 2026-04-15 04:15:23

911

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If a scalar field is continuous at a point, then is it also differentiable at that point?

Published on 15 Apr 2026 - 4:15

score 41 · Answer 13 · 2026-03-25 20:33:47

41

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Struggling to find implicitly-defined function and its second derivative

Published on 25 Mar 2026 - 20:33

score 85 · Answer 14 · 2026-04-25 13:31:16

85

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Is the function $f(x)=\lfloor\sin(\ln(x+2)\rfloor$ differentiable at $x=0$?

Published on 25 Apr 2026 - 13:31

score 197 · Answer 15 · 2026-04-16 21:08:16

197

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$f : \mathbb R \to [-2,2]$ be a twice differentiable with $f(0)^2+ f'(0)^2=85$

Published on 16 Apr 2026 - 21:08

List Question

Prob. 4, Exercises 8.14, in Apostol's CALCULUS Vol II: Computing the gradient vector and a directional derivative for a scalar field

Prob. 5, Exercises 8.14, in Apostol's CALCULUS Vol II: Find constants such that the directional derivative

Positive semi-definiteness of the Jacobian of the partial derivatives of distinct convex functions

Evaluate the Limit $\lim_{x \to 0}\frac{x}{\sqrt{1-e^{-x^2}}}$

Directional derivative.

Prob. 6, Exercises 8.14, in Apostol's CALCULUS Vol II: Given a scalar field differentiable at a point ...

Nonstandard-Analysis: Showing L'Hospital

Can limit be taken inside a function which has a removable Discontinuity

Can the gradient of a non-constant scalar field be zero?

Prob. 9, Exercises 8.14, in Apostol's CALCULUS Vol II: If the derivatives of a scalar field on an open ball vanish in $n$ independent directions,

Prob. 10, Exercises 8.14, in Apostol's CALCULUS Vol II: If the gradient of a differentiable scalar field is zero on an open ball, . . .

If a scalar field is continuous at a point, then is it also differentiable at that point?

Struggling to find implicitly-defined function and its second derivative

Is the function $f(x)=\lfloor\sin(\ln(x+2)\rfloor$ differentiable at $x=0$?

$f : \mathbb R \to [-2,2]$ be a twice differentiable with $f(0)^2+ f'(0)^2=85$

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