Math 214
Homework for Sections 2.10 and 4.1
Spring 2016
This problem set is out of 32 points. It is due on Thursday, April 7.
Problem 1. (5 points) Use the Implicit Function Theorem to determine at which points
in R3 the surface f (x, y, z) = x3 + 3y 2 + 8xz 3 − 3z 3 y − 1 = 0 can be expressed locally as a
function z = g(x, y).
Problem 2. (7 points) What can you say about solving the equations
x 2 − y 2 − u3 + v 2 + 4 = 0
2xy + y 2 − 2u2 + 3v 4 + 8 = 0
   
x
2
y  1
  
for u and v in terms of x and y in a neighborhood of the solution 
u = 2?
v
1
Problem 3. (10 points) Complete Problem 4.1.6a. Complete part b for [0, a] only.
Problem 4. (10 points) Complete Problem 4.1.10 in the text.
1