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MATH 51 MIDTERM II
November 17, 2005
Name:
Numeric Student ID:
Instructor’s Name:
I agree to abide by the terms of the honor code:
Signature:
Instructions:
Print your name, student ID number and instructor’s name in the space
provided. During the test you may not use notes, books or calculators. Read each
question carefully and
show all your work
; full credit cannot be obtained without
suﬃcient justiﬁcation for your answer unless explicitly stated otherwise. Underline your
ﬁnal answer to each question. There are 9 questions. You have 90 minutes to do all the
problems.
Question
Score
Maximum
1
10
2
6
3
8
4
6
5
10
6
10
7
15
8
10
9
10
Total
85

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*Sign up* Question 5 of 9, Page 2 of 4
Solutions
1. Consider the function
f
(
x, y
) =
x
4
y
3
and the point
P
= (1
,
1
,
1) on its graph.
(a) Write down the equation of the tangent plane at the graph of the function at
the point
P
.
(b) Using your answer from (a), write down an expression for the change, Δ
z
, in
z
=
f
(
x, y
) depending on Δ
x

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