MATH 2203 Lecture 9: Chpt. 11 Vector Functions and Beginning of Chpt. 12 Functions of Several Variables

Let F(x, y, z) (3ex sin(y))ì + (3ex cos(y))j + 7z2k. Evaluate the integral F . ds, where c(t) = (7/t. t, exp (VE), o s t s 1. (Note that exp (u-eu.) F.ds

11 Find the point on the curve r(t) (12sin t)l (12cos tj 5t k at a distance of 13n units along the curve from the point (0, -12, 0) in the direction opposite to the direction of increasing arc length. 12 Compute T, N, and K at the point 1 of the twisted cubic with position 2' 3 vector r t i j at k. TT 13 Find T, N, Br K, and T for the space curve r() (cos3t)i (sin3 t j, o t 14 Given r t) et cos t)i (et sin t)j 2e k, write a in the form a aTT aNN atta 0 without finding Tand N. 15 Given r(t) (e t cos t)l (et sin tj 2k. Find r, T, N, and B at t 0. Then find the equations for the osculating, normal, and rectifying planes at t 0.