MATH 222 Midterm: MATH 222 KSU Test 2s99

• School: Kansas State University
• Department: Mathematics
• Course: MATH 222
• Professor: All

Document Summary

To receive credit you must show your work. (15) 1. A quantity q depends upon x and y according to q = x2e xy. Suppose x and y are changing with time t and at a certain instant you know that. 2 x = 3 , y = 1 , this instant. dx dt. Use the chain rule to calculate dq dt at. Let f (x, y) = x3y + 2xy2 6x + 2y + 3 : find the gradient vector eld of f . F : suppose you are moving along a straight line through the point p (1, 2) to- ward the point q(4, 1) . Use the method of lagrange multipliers to nd the largest value and the smallest value of f (x, y, z) = x + 2y + z2 on the ellipsoid x2 + y2 + 2z2 = 20 .