MATH 211 Final: MATH 211 Amherst F15M211 2802 29ZhangFinal

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 211
• Professor: All

Document Summary

You are not allowed to use books, notes or calculators. You must explain your answers com- pletely and clearly to get full credit. Name: (10 points) (a) (5 points) find the distance between the parallel planes x 3y + 2z = 2 and. 3x 9y + 6z = 9. (b) (5 points) find the acute angle between the planes x + 2y z = 2 and x + y = 0. Express this angle in exact degrees: (10 points) (a) (5 points) the trajectory of a particle moving through space is given by the vector function. Explain: (10 points) (a) (5 points) let f (x, y) = ln(xy). Suppose x = g(s, t), y = h(s, t), where g and h are di erentiable functions. Find at (s, t) = (1, 2) given the following information. Z 1 x2 x sin(y2)dydx. (b) (5 points) rewrite the following triple integral in the order dydzdx.