Problem 8. Let F(x, y, 2) = (2x2 + sin(y), a cos(y), x²) %3D |(8A) Show that F is conservative. (8B) Find F dr where C is the straight line from (0,0,0) to (-1, 7, 1).

5. (а) Find the directional derivative of f at P in the direction of ā if f(x,y) = y In(x) ; P(1,4); ā = -3i +3j.

How large should n be to guarantee that the Trapezoidal Rule approximation to 14x – 60z? – læ + 3)dx is accurate to within 0.1. 5 n = How large should n be to guarantee that the Simpsons Rule approximation to | (-24 – 14x – 60z? – læ + 3)dx is accurate to within 0.1. n = Hint: Remember your answers should be a whole numbers, and Simpson's Rule requires even values for n

11) Find a function y-f (x) that satisfies both conditions: dy = 6x-4x+5, f(-1) =3 dx dy 2 3 ==++2x-1, f (1) =1 dx x x"