MATH1510 Lecture : Maths assignment-1

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

(1 pt) Use the contour diagram of f in the figure below to decide if the specified directional derivatives below are positive, negative, or approximately zero. (a) At point (-2, 2), in direction -i : f u is ? (b) At point (0,-2). in direction -j: f u is (c)At point (-1,1), in direction -i + j f u is (d) At point (-1, 1). in direction j + j : f u is (e) At point (0, -2). in direction j + 2 j f u is ? (f) At point (0, -2). in direction j - 2 j : f u is ?

(1 point) lf C is the curve given by r (t) = (1 + 5 sin ) i + (1 + 1 sin*) j + (1 + 3 sin*) k, 0 t $ and F is the radial vector field F(x, y, z) = xi + yj + zk, compute the work done by F on a particle moving along C.