MTH 1001 Lecture Notes - Junkers J.I

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 line integral F (x, y) = y2 I - 2xy j where C is the cure r (t) = t3 I + t j 0 t 2

Let F(x, y) = x2+y2" x2 + y2 Show that ON.Oy where M-2yy2 and N-r2. (a) ON 2+2)2 dy 2212 ind "IF-dr (b) lf r(t)=cos(t)i+sin(t)j for osts, if r(t)= cos(t)i-sin(t)j for o stsn, findl F.dr (c) (d) If r(t) = cos(t)i + sin(t)j for 0 t 2n, find F . dr