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Math 148 Lab Assignment 7: §10.1–10.2
Directions: You may work in groups of 2–3 to complete this assignment. Answer
each question completely. Show all work to receive full credit, and circle your
final answer.
1. Find the largest possible domain and the corresponding range of each function. Sketch
the domain in the xy-plane.
p
(a) f (x, y) = 4 − x2 − y 2
√
(b) g(x, y) = e−
x
1
2. Consider the function f defined by f (x, y) = 1 + x2 + y 2 .
(a) Describe the level curves f (x, y) = k, and determine the possible values of k.
(b) Sketch the level curves for k = 1, 2, 10.
3. Evaluate each limit.
(a)
lim
(x2 y 3 − 3xy)
(x,y)→(2,−1)
(b)
x2 − y 2
(x,y)→(−1,−2) 2xy + 2
lim
2
4. Evaluate the limit
lim
2xy
+ xy
(x,y)→(0,0) x3
if it exists. If the limit does not exist, explain your answer.
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