MATH 2210 Midterm: MATH 2210 Cornell 2210 2013 Fall prelim2 solution Exam
Document Summary
You have 1 hour 30 minutes to complete this exam. You are free to use results from the lectures, but you should clearly state any theorems you use. The exam is printed on both sides of the paper. 2 ) (a) state what it means for a function f : r3 r to be continuous. (b) show that f is continuous. You may use the fact that the functions ex and cos(x) are continuous functions of one variable. (c) either nd lim(x,y,z) (0,0,0) f (x, y, z) or show that it does not exist. (d) calculate. 1 (4) let f : r2 r be a c 1 function with. 1 + y2 (a) draw the level curve f (x, y) = k for the value k = 2. (b) calculate f . (c) a pirate, captain x, is marooned on the island. He is standing at the point ( 1, 1, 2) and wants to descend as quickly as possible.
