Question

Temperature in a point is given by $T=xyz$. If you are in the point $(1,1,1)$, in which direction you should go to keep the same temperature?

score 938 · Answer 1 · 2026-04-14 10:43:57

Temperature in a point is given by $T=xyz$. If you are in the point $(1,1,1)$, in which direction you should go to keep the same temperature?

score 1.9k · Answer 2 · 2026-04-24 13:56:02

1.9k

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Is the local max point also a global max?

Published on 24 Apr 2026 - 13:56

score 190 · Answer 3 · 2026-05-10 23:31:39

190

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$\iint (x+y)e^{xy} dA$ . where A is region enclosed by $x-y = 1$, $x-y=4$, $xy = 1$, $xy=2$

Published on 10 May 2026 - 23:31

score 3.6k · Answer 4 · 2026-05-11 08:19:08

3.6k

Views

Differentials in Multivariable Calculus

Published on 11 May 2026 - 8:19

score 107 · Answer 5 · 2026-04-15 05:51:15

107

Views

How to find an area between $x =\frac 12$ on the right, $y = \frac x{\sqrt3}$ above and by the circle $x^2 + y^2 = 2x$ with polar coordinates?

Published on 15 Apr 2026 - 5:51

score 58 · Answer 6 · 2026-05-10 19:00:40

58

Views

a question about gradient

Published on 10 May 2026 - 19:00

score 101 · Answer 7 · 2026-05-10 18:06:17

101

Views

Proof inequality $\frac{\sqrt{\pi}}{2}\sqrt{1-e^{-a^2}} < \int_0^a e^{-x^2}dx < \frac{\sqrt{\pi}}{2}\sqrt{1-e^{-2a^2}}$

Published on 10 May 2026 - 18:06

score 88 · Answer 8 · 2026-04-13 08:07:26

88

Views

integrate over one cordinate like partial derivative

Published on 13 Apr 2026 - 8:07

score 1k · Answer 9 · 2026-05-11 09:10:04

1k

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Evaluate $\iiint_{[0,1]^3}\frac{dx\,dy\,dz}{(1+x^2+y^2+z^2)^2}$

Published on 11 May 2026 - 9:10

score 157 · Answer 10 · 2026-04-15 12:13:07

157

Views

Points of Confusion About Second-Order Taylor Formula of Taylor's Theorem For Many Variables

Published on 15 Apr 2026 - 12:13

score 7.5k · Answer 11 · 2026-04-16 08:10:52

7.5k

Views

Show that the product of the Jacobian and the inverse Jacobian is 1

Published on 16 Apr 2026 - 8:10

score 131 · Answer 12 · 2026-04-16 13:17:05

131

Views

Change of variable in double integrals $\iint_S f(x,y) \,dx \,dy$, where $S=\{(x,y)|x^2\leq y,-1 \leq x\leq 1\}$.

Published on 16 Apr 2026 - 13:17

score 463 · Answer 13 · 2026-04-24 15:51:29

463

Views

Maximizing Profit with two limited products

Published on 24 Apr 2026 - 15:51

score 288 · Answer 14 · 2026-04-13 01:44:39

288

Views

Multivariable Calculus: Lagrange function

Published on 13 Apr 2026 - 1:44

score 869 · Answer 15 · 2026-04-16 03:03:55

869

Views

Limit of $\frac{y^4\sin(x)}{x^2+y^4}$ when $(x,y) \to (0,0)$

Published on 16 Apr 2026 - 3:03

List Question

Temperature in a point is given by $T=xyz$. If you are in the point $(1,1,1)$, in which direction you should go to keep the same temperature?

Is the local max point also a global max?

$\iint (x+y)e^{xy} dA$ . where A is region enclosed by $x-y = 1$, $x-y=4$, $xy = 1$, $xy=2$

Differentials in Multivariable Calculus

How to find an area between $x =\frac 12$ on the right, $y = \frac x{\sqrt3}$ above and by the circle $x^2 + y^2 = 2x$ with polar coordinates?

a question about gradient

Proof inequality $\frac{\sqrt{\pi}}{2}\sqrt{1-e^{-a^2}} < \int_0^a e^{-x^2}dx < \frac{\sqrt{\pi}}{2}\sqrt{1-e^{-2a^2}}$

integrate over one cordinate like partial derivative

Evaluate $\iiint_{[0,1]^3}\frac{dx\,dy\,dz}{(1+x^2+y^2+z^2)^2}$

Points of Confusion About Second-Order Taylor Formula of Taylor's Theorem For Many Variables

Show that the product of the Jacobian and the inverse Jacobian is 1

Change of variable in double integrals $\iint_S f(x,y) \,dx \,dy$, where $S=\{(x,y)|x^2\leq y,-1 \leq x\leq 1\}$.

Maximizing Profit with two limited products

Multivariable Calculus: Lagrange function

Limit of $\frac{y^4\sin(x)}{x^2+y^4}$ when $(x,y) \to (0,0)$

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