Question

Prove that $\lim_{(x,y) \rightarrow (0,0)}\frac{xy}{\sqrt{x^2+y^2}}$ exists without using polar coordinates

score 109 · Answer 1 · 2026-04-16 20:00:08

109

Views

Prove that $\lim_{(x,y) \rightarrow (0,0)}\frac{xy}{\sqrt{x^2+y^2}}$ exists without using polar coordinates

Published on 16 Apr 2026 - 20:00

score 179 · Answer 2 · 2026-04-22 19:47:35

179

Views

How $||\nabla f(x) - \nabla f(\overline{x})||\le L|x-\overline{x}|$ implies $(\nabla f(x) -\nabla f(\overline{x}))^Tp_k\le L|x-\overline{x}||p_k|$

Published on 22 Apr 2026 - 19:47

score 548 · Answer 3 · 2026-03-30 12:22:50

548

Views

gradient descent method with linear exact search we have $\nabla^t f(x^k)\nabla f(x^{k+1})=0$

Published on 30 Mar 2026 - 12:22

score 246 · Answer 4 · 2026-04-15 20:34:01

246

Views

What is the general expression for the gradient of $\dfrac{1}{2} x^TA(x)x$?

Published on 15 Apr 2026 - 20:34

score 232 · Answer 5 · 2026-04-09 03:15:18

232

Views

Fundamental theorem of calculus on double integrals

Published on 09 Apr 2026 - 3:15

score 28 · Answer 6 · 2026-04-08 20:48:50

28

Views

Computing a composition of factors

Published on 08 Apr 2026 - 20:48

score 138 · Answer 7 · 2026-04-11 16:04:30

138

Views

How to apply the divergence theorem to a parametric surface

Published on 11 Apr 2026 - 16:04

score 2.7k · Answer 8 · 2026-04-17 14:52:40

2.7k

Views

Gradient and Hessian of $x x^T$ w.r.t. $x$, where $x \in \mathbb{R}^{n \times 1}$,?

Published on 17 Apr 2026 - 14:52

score 216 · Answer 9 · 2026-04-16 05:18:33

216

Views

Solutions to $\frac{Q\partial P}{x\partial x}-\frac{P\partial Q}{x\partial x}-\frac{Q\partial P}{y\partial y}+\frac{P\partial Q}{y\partial y}=0$

Published on 16 Apr 2026 - 5:18

score 512 · Answer 10 · 2026-04-16 16:27:09

512

Views

Find the stationary points of $f(x) = 2x_1^3 -3x_1^2 -6x_1x_2(x_1-x_2-1)$ and see which of them are maxima or minima

Published on 16 Apr 2026 - 16:27

score 434 · Answer 11 · 2026-04-16 11:05:36

434

Views

Prove that the function $f(x) = (x_2-x_1^2)^2 +x_1^5$ has only one stationary point which is not extreme

Published on 16 Apr 2026 - 11:05

score 243 · Answer 12 · 2026-04-17 07:04:56

243

Views

Minimize $f(x) = x_1^2 -x_1x_2+2x_2^2-2x_1+e^{x_1+x_2}$

Published on 17 Apr 2026 - 7:04

score 40 · Answer 13 · 2026-04-15 19:52:18

40

Views

Are points of the form $\overline{x} = (1,x_2)$ extremes of $f(x) = (x_1-1)^2x_2$?

Published on 15 Apr 2026 - 19:52

score 620 · Answer 14 · 2026-04-14 16:07:52

620

Views

Solution to the differential equation $(2x^2+xy-2y^2)dx+(3x^2+2xy)dy=0$

Published on 14 Apr 2026 - 16:07

score 1.4k · Answer 15 · 2026-04-14 00:23:49

1.4k

Views

Inner product of multivariable functions

Published on 14 Apr 2026 - 0:23

List Question

Prove that $\lim_{(x,y) \rightarrow (0,0)}\frac{xy}{\sqrt{x^2+y^2}}$ exists without using polar coordinates

How $||\nabla f(x) - \nabla f(\overline{x})||\le L|x-\overline{x}|$ implies $(\nabla f(x) -\nabla f(\overline{x}))^Tp_k\le L|x-\overline{x}||p_k|$

gradient descent method with linear exact search we have $\nabla^t f(x^k)\nabla f(x^{k+1})=0$

What is the general expression for the gradient of $\dfrac{1}{2} x^TA(x)x$?

Fundamental theorem of calculus on double integrals

Computing a composition of factors

How to apply the divergence theorem to a parametric surface

Gradient and Hessian of $x x^T$ w.r.t. $x$, where $x \in \mathbb{R}^{n \times 1}$,?

Solutions to $\frac{Q\partial P}{x\partial x}-\frac{P\partial Q}{x\partial x}-\frac{Q\partial P}{y\partial y}+\frac{P\partial Q}{y\partial y}=0$

Find the stationary points of $f(x) = 2x_1^3 -3x_1^2 -6x_1x_2(x_1-x_2-1)$ and see which of them are maxima or minima

Prove that the function $f(x) = (x_2-x_1^2)^2 +x_1^5$ has only one stationary point which is not extreme

Minimize $f(x) = x_1^2 -x_1x_2+2x_2^2-2x_1+e^{x_1+x_2}$

Are points of the form $\overline{x} = (1,x_2)$ extremes of $f(x) = (x_1-1)^2x_2$?

Solution to the differential equation $(2x^2+xy-2y^2)dx+(3x^2+2xy)dy=0$

Inner product of multivariable functions

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