Question

How to Find the integral $\int_{S}−(xy^2)~dydz + (2x ^2 y)~dzdx − (zy^2)~dxdy$ where is the portion of the sphere $x^2 + y^2 + z^2 = 1$

score 116 · Answer 1 · 2026-03-26 06:07:58

116

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How to Find the integral $\int_{S}−(xy^2)~dydz + (2x ^2 y)~dzdx − (zy^2)~dxdy$ where is the portion of the sphere $x^2 + y^2 + z^2 = 1$

Published on 26 Mar 2026 - 6:07

score 142 · Answer 2 · 2026-03-25 22:26:45

$f$ is a $k$-Lipschitz continuous function & continuously differentiable $\forall x \in \mathbb{R}^n$. Prove/disprove: $||D_{f}(x)||_{op} \leq k$

score 150 · Answer 3 · 2019-01-23 15:36:05

150

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134

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List Question

How to Find the integral $\int_{S}−(xy^2)~dydz + (2x ^2 y)~dzdx − (zy^2)~dxdy$ where is the portion of the sphere $x^2 + y^2 + z^2 = 1$

$f$ is a $k$-Lipschitz continuous function & continuously differentiable $\forall x \in \mathbb{R}^n$. Prove/disprove: $||D_{f}(x)||_{op} \leq k$

Not a manifold: $x^3 + y^3 - 3xy = 0$

Surface integral of an infinitesimal volume = 0?

Deriving analytic expression for magnetic field & flow lines of bar magnet.

Formula of the gradient of vector dot product

Vector Calculus proof part derivation.

Basis vectors of coordinate systems

"Slippery Slope" - a Parametric Trajectory problem

How to find a unit normal vector to the given curve?

An example of divergence in spherical coordinates

Is it true that $(\Delta\varphi)\phi=\nabla \cdot(\nabla\phi)\varphi-\nabla\phi\cdot\nabla\varphi$ for complex-valued functions $\phi$ and $\varphi$?

Gradient is orthogonal to the circle

Basis vectors in different coordinates

Find the amplitude of the oscillation of the particle.

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