MAT 106 Lecture 7: Trig Notes Chapter 8

Blai the diver 16.5 Exercises 1-8 Find (a) the curl and (b) the divergence of the vector field. 1, F(x, y, z) = xyz i-ry k 12 3, F(x, y, z) = xye' i + yze'k 4. F(x, y, z) = sin yzi + sin zxjt sin xyk (r i+ 6. F(x, y, z) = exy sin z j + y tan-i (x/z) k 7. F(x, y, z) =

Evaluate the line integralF dr, where C is given by the vector function r(t) F(x, y, z) = x i + y j + xy k, r(t) = sin(t) + cos(t)jt t k, 0 t π

5. (4 points) Evaluate the derivative of the following: a) r(x)= 「 In(5x2-10x) 10x-10 b) c(x) J(2x 3x2)sin(x2 +x3)dx (10 points) Use u-substitution to evaluate the following integral: Tt/8 6. tan2x dx = Jt/12