Evaluating a Flux Integral In Exercises 25-30, find the flux of F across S,
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Calculus
- Image is attached.plz solvearrow_forwardSubject differential geometry Let X(u,v)=(vcosu,vsinu,u) be the coordinate patch of a surface of M. A) find a normal and tangent vector field of M on patch X B) q=(1,0,1) is the point on this patch?why? C) find the tangent plane of the TpM at the point p=(0,0,0) of Marrow_forward人工知能を使用せず、 すべてを段階的にデジタル形式で解決してください。 ありがとう SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE CHATGPT Find the integral of the vector function F(t)=(f.,cost)arrow_forward
- An exercise on the gradient of a vector field Consider a potential function of the form • U(x, y) = Ax² + Bxy + Cy² + Dx + Ey+F Compute the gradient vector VU (x, y). Answer: U(x, y) = (2Ax+By+D,Bx+2C y +E) ⚫ Pick some values for A, B, C, D, E, F out of a hat (keep it simple!) • Ask yourself: does there exist a point (x, y) at which the gradient vector VU(x, y) is the zero vector? If so, is that point unique? • Repeat as necessary. • What conditions on A, B, C, D, E, F are necessary and sufficient for the existence of a point (x, y) at which VU (x, y) is the zero vector? If that point exists, is it unique?arrow_forwardhow do i solve the attached calculus problem?arrow_forwardLinear Algebra question is attached.arrow_forward
- Determine whether the line integral of each vector field (in blue) along the semicircular, oriented path (in red) is positive, negative, or zero. Positive Positive Zero Zero Negative Positive - 1.arrow_forwardCompute the flux of the vector field F(x, y, z)-6i+6j+ 4k through the rectangular region with corners at (1,0,0). (1,1,0), (1,1,2), and (1,0,2) oriented in the positive x direction, as shown in the figure. Flux y/7215 Z (Drag to rotate)arrow_forwardShow that the vector-valued function shown below describes the function of a particle moving in a circle of radius 1 centered at a point (5,5,3) and lying in the plane 3x+3y-6z = 12arrow_forward
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