Calculus 3

Final answer only

no explanation needed

Section 13.3: Problem 5 (1 point) Let F = (5ry, 3y ) be a vector field in the plane, and O the path y = 82 joining (0, 0) to (1, 8) in the plane. A. Evaluate J F . dr 74 B. Does the integral in part (A) depend on the path joining (0, 0) to (1, 8)? (y)Section 13.3: Problem 9 (1 point) The figure shows level curves of a function f(I, y). 4 (a) Draw gradient vectors at P and Q. Is V f(P) longer than, shorter than, or the same length as V f(Q)?|? 14 2 (b) If C is the line segment from P to Q, then longer than Vf. dr = 0 shorter than the same length as 3 (c) If C is any piecewise-smooth path from P to T' to Q, then (d) If C is any piecewise-smooth path from S to P, then 37 28 (e) If C is any piecewise-smooth closed path from P to Q to T' to S to P, then (Click on graph to enlarge)Section 13.3: Problem 10 (1 point) Consider the vector field F in the figure and the closed circular path C oriented counter-clockwise. 4 (a) Is F . d positive, negative, or zero? ? (b) True or False: F = grad f for some function f. Hint: use your answer to part (a). ? ? (c) Which of the following formulas best fits F? True False T. OA. F = OB. F = (x2 + 1/2)2 Oc. F = -ri -yj 1 OD. F = -yi+Ij H (Click on graph to enlarge)Section 13.3: Problem 11 (1 point) Determine whether each of the following vector fields appears to be path independent (conservative) or path dependent (not conservative). ? ? 2 (Click on a graph to enlarge it) path independent path dependent Note: You can earn 50% partial credit for 3 - 5 correct answers. Preview My Answers Submit AnswersSection 13.4: Problem 4 (1 point) Use Green's Theorem to evaluate the line integral of F = (x*, 8x) around the boundary of the parallelogram in the following figure (note the orientation). With Io = 4 and 10 = 4. (To. 0) for de + 8rdy 0\fSection 13.2: Problem 2 (1 point) Evaluate the line integral Bry" ds, where C is the right half of the circle r' t y' = 9. 34992 7Section 13.2: Problem 7 (1 point) Evaluate the line integral [ F . dr, where F(I, y, 2) = -5sin(x) i -3 cos(y) j + 4xzk and C is given by the vector function r(t) =Pi-t'j ttk, 0