01:640:251 Lecture 22: 15.4 Multivariable Calculus

Problem 6 A) For each vector field, identify its picture from those given below F(x,y) = x2 i+y2 j F(x.yjacos(x)i + siayj ー F(x,y)sin(x)i + yj 40---25 50 25 5 50 1//ぃぃぃ 、\\\ \ u l l B) Let F(x,y,z) (x)it (r)jt ㈣kbe a vector field in R, Find the work done by Fin moving an object along the path C given by r(r)kfor 0 s t s L C) If F were a conservative vector field, what would be the work done in moving the object around the circular path given by s()cos+sin(r)j+2k from i-0 to2x?

Evaluate the integral to the origin. c F dr for F = 6xy6 + 5x2ys j on the curve C consisting of the x-axis from x tox-2 the parabola y = 4-2 up to the y a s, and they a s down

10 points) Suppose that f(x) is a 2L periodic function which is piecewise continuous on ecew s ALWAYS TRUE? A. The Fourier series representation of f(x) always converges to f(x) at every point in I-L, L) B. If f(a) sin(4Tx/L), then the Fourier series for f(x) is exactly sin(4a/L). C. If f (0 ) lim = 4 and f(0+)-lim-2, the Fourier series for f(z) must converge z--o t0 6 at 0, r) is an odd function, then the Fourier sine series for the function is simply zero. D. If f(