calculus 3

final answer only , no explanation needed

Section 13.1: Problem 1 (1 point) Compute the gradient vector fields of the following functions: A. f(I, y) = 613 + 87 = (6 'I)/4 it B. f (I, y) = ry Vf(=, y) = C. f(r, y) = 6: + By Vf(I, y) = it D. f(x, y, =) = 6x + 8y + 10z Vf(z, y) = it it k E. f(x, y, 2) = 613 + 817 + 1023 Vf(z, y, =) = it j+ kSection 13.1: Problem 4 (1 point) Write a formula for a two-dimensional vector field which has all vectors parallel to the c-axis and all vectors on a vertical line having the same magnitude. VSection 13.1: Problem 5 (1 point) Each vector field shown is the gradient of a function f(I, y). Match the gradient field of each function to the contour plot of that function. 1. Choose v 2. Choose v 3. Choose v A B C (Click on a graph to enlarge it.) Note: In order to get credit for this problem all answers must be correct. Preview My Answers Submit Answers You have attempted this problem 0 times. You have 4 attempts remaining.Section 13.1: Problem 6 (1 point) Each vector field shown shown represents the force on a particle at different points in the plane as a result of another particle at the origin. Match each vector field with its description. ? | 1. An attractive force whose magnitude decreases as distance increases. ? v 2. A repulsive force whose magnitude increases as distance increases. ? v 3. A repulsive force whose magnitude decreases as distance increases. ? 4. An attractive force whose magnitude increases as distance increases. ? A B C D (Click on a graph to enlarge it.)Section 13.1: Problem 7 (1 point) Match each vector field with its graph. ? v 1.F -zi+ yj ? v 2. F = Ii + yj + zk ? v 3.F= vitzj ? v AF= 1 ? v 5.F_ Vitzj ? v 6. F = zi + yj + zk ? 37 7 - -2.50 _0.0g 0.00 _ 0.Do -2 50 -2/50 -2 50 3435 245010 2.65 - A B C 150 - 3.00 2.50 - 0.30 0.bo 0.DO -2 50 -3/00 -2/90 8.Gago 3,000 10 3.10Section 12.7: Problem 11 (1 point) Find the volume of the solid that lies within the sphere ' + y' + 2" = 36, above the ry plane, and outside the cone 2 = 4VI- + . 13.50Section 12.7: Problem 12 (1 point) Find an equation for the paraboloid & = c' + y in spherical coordinates. (Enter rho, phi and theta for p, and d, respectively.) equation: cos(ethera)