Math 231 Fall 2017 Homework 8 Due Thursday October 26. Write clearly, and when possible, encase your final answer in a colored rectangle. Avoid using calculator, it won't be allowed in the tests (however, double checking your answers in the homework is not a bad idea). 1. Determine whether the following limits exist. x2 + 2xy . (x,y)(1,1) x2 + y 2 x2 + 2y 2 b) lm . (x,y)(0,0) x2 + y 2 x4 y 4 . c) lm (x,y)(0,0) x2 + y 2 a) lm 4. Set f (x, y) = max{x, y}. Determine at which points pute them. f x and f x exist. Com- 5. Set f (x, y, z) = ||(x, y, z)||. Determine when its partial derivatives fx , fy , fz exist and compute them. 6. Suppose there is a function g(x, y) for which you know the level curves. If one of them is the line x = 1, find the value of g/x along that line. 1