MATH 253 Study Guide - Midterm Guide: Directional Derivative

• School: UBC
• Department: Mathematics
• Course: MATH 253
• Professor: All

Document Summary

You have 150 min to solve 7 problems. Please note: write your name/student id clearly, write only on one side of the paper in the space design for it. Use the last few pages of the exam for calculations. 1: find the limit or show that it does not exist lim (x,y,z) (0,0,0) xy + yz2 + xz2 x2 + y2 + z4. 2. (a) compute the gradient of the function f (x, y) = z y x cos(t2) dt (b) use the gradient to approximate f (0, 0. 1). 5: if z = f (x, y) where x = s + t and y = s t show that (a) (b) (zx)2. 7: find the direction in which the directional derivative of the function at point (0, 2) has the value 1. f (x, y) = ye xy. 5. a find the critical points of the function f (x, y) = (x2.