Question

Given $f(x,y)=5+2x+4y+x^2+y^2+(x^2y^4)^\frac15$, show that it is differentiable at $(0,0)$.

score 321 · Answer 1 · 2026-04-16 17:32:56

321

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Given $f(x,y)=5+2x+4y+x^2+y^2+(x^2y^4)^\frac15$, show that it is differentiable at $(0,0)$.

Published on 16 Apr 2026 - 17:32

score 102 · Answer 2 · 2026-04-16 07:21:24

102

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Prob. 21, Exercises 8.9, in Apostol's CALCULUS vol. II: If the directional derivative of a scalar field vanishes . . .

Published on 16 Apr 2026 - 7:21

score 427 · Answer 3 · 2026-04-12 10:38:57

427

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How to calculate an optimal combination of metals based on price

Published on 12 Apr 2026 - 10:38

score 47 · Answer 4 · 2026-04-08 21:42:39

47

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About the solvability of non-analytical equations with new "helper" functions

Published on 08 Apr 2026 - 21:42

score 43 · Answer 5 · 2026-04-17 03:13:03

43

Views

Why $B_\epsilon(d)\not\subset G'\not\rightarrow B_\epsilon(d)\subset G'^c$?

Published on 17 Apr 2026 - 3:13

score 591 · Answer 6 · 2026-04-14 18:55:51

591

Views

Prob. 22, Exercises 8.9, in Apostol's CALCULUS vol 2: There is no scalar field with all non-zero directional derivatives at a single point

Published on 14 Apr 2026 - 18:55

score 532 · Answer 7 · 2026-04-08 23:17:22

532

Views

Why is Axiom of Choice "a convenient and safe labour-saving device"?

Published on 08 Apr 2026 - 23:17

score 48 · Answer 8 · 2026-04-16 19:23:37

48

Views

What is an "optimal convergence rate" ?

Published on 16 Apr 2026 - 19:23

score 2.9k · Answer 9 · 2026-04-16 11:24:47

2.9k

Views

Why $SO(3,\mathbb{R})$ is $3$-dimensional?

Published on 16 Apr 2026 - 11:24

score 193 · Answer 10 · 2026-04-11 14:34:56

193

Views

Inequality in a scalar product.

Published on 11 Apr 2026 - 14:34

score 44 · Answer 11 · 2026-04-14 22:50:17

44

Views

Suppose $A=\bigcup_i A_i$ is f-invariant. Then $f^n(A_i)\subseteq A$ for all $n\in\mathbb{N}$?

Published on 14 Apr 2026 - 22:50

score 54 · Answer 12 · 2026-04-17 13:54:37

54

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Show that $\epsilon ( integer(a/\epsilon) - integer(b/\epsilon) )= a - b + O(\epsilon)$

Published on 17 Apr 2026 - 13:54

score 65 · Answer 13 · 2026-04-16 12:13:03

65

Views

Find the limit: $\lim_{x \rightarrow \infty} \frac{|x|^{n} - (1 + |x|^2)^{\frac{2}{n}}}{(1 + |x|^2)^{\frac{2}{n}}}.$

Published on 16 Apr 2026 - 12:13

score 207 · Answer 14 · 2026-04-16 03:54:00

207

Views

Length of a partition being equal to the length of the interval

Published on 16 Apr 2026 - 3:54

score 8.6k · Answer 15 · 2026-04-23 00:12:56

8.6k

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Deriving Rodrigues Formula and Generating function of Hermite Polynomial from $H_n(x)= e^{x^2/2}(x-\frac{d}{dx})^ne^{-x^2/2}$

Published on 23 Apr 2026 - 0:12

List Question

Given $f(x,y)=5+2x+4y+x^2+y^2+(x^2y^4)^\frac15$, show that it is differentiable at $(0,0)$.

Prob. 21, Exercises 8.9, in Apostol's CALCULUS vol. II: If the directional derivative of a scalar field vanishes . . .

How to calculate an optimal combination of metals based on price

About the solvability of non-analytical equations with new "helper" functions

Why $B_\epsilon(d)\not\subset G'\not\rightarrow B_\epsilon(d)\subset G'^c$?

Prob. 22, Exercises 8.9, in Apostol's CALCULUS vol 2: There is no scalar field with all non-zero directional derivatives at a single point

Why is Axiom of Choice "a convenient and safe labour-saving device"?

What is an "optimal convergence rate" ?

Why $SO(3,\mathbb{R})$ is $3$-dimensional?

Inequality in a scalar product.

Suppose $A=\bigcup_i A_i$ is f-invariant. Then $f^n(A_i)\subseteq A$ for all $n\in\mathbb{N}$?

Show that $\epsilon ( integer(a/\epsilon) - integer(b/\epsilon) )= a - b + O(\epsilon)$

Find the limit: $\lim_{x \rightarrow \infty} \frac{|x|^{n} - (1 + |x|^2)^{\frac{2}{n}}}{(1 + |x|^2)^{\frac{2}{n}}}.$

Length of a partition being equal to the length of the interval

Deriving Rodrigues Formula and Generating function of Hermite Polynomial from $H_n(x)= e^{x^2/2}(x-\frac{d}{dx})^ne^{-x^2/2}$

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