Name(s):
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Math 148 Lab Assignment 8: §10.3–10.4
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 first partial derivatives of each function.
(a) f (x, y) = x4 + x2 y 2 + y 4 + ln(x2 + y 2 )
(b) f (x, y) =
x−y
x+y
(c) f (x, y) = ey tan(x2 y 3 )
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2. Find all second partial derivatives of f (x, y) = (x2 + y 2 )3/2 .
3. Find the linearization of f (x, y) = ln(2x + y) at (−1, 3, 0) and use it to approximate
f (−1.1, 2.9).
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4. Find the linearization of the vector function F~ (x, y) = hye−x , sin x + cos yi at (0, 0) and
use it to approximate F~ (0.1, −0.1).
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