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34B
Practice for Midterm II
Winter 2006
Instructor: Prof. Wei
Midterm II: Friday, March 3, covering Sections 12.312.6 and 13.113.8
Practice Problems
1. (a) Find the general solution of
y
00
(
t
) = 12
t

2 and the particular solution for
which
y
(0) = 3 and
y
(1) = 5.
(b) Find the solution of the diﬀerential equation
y
0
= 2(3

y
) satisfying the initial
condition
y
(0) = 7.
2. Find the local max and min of
x
+ 9
x

1
. Clearly show how you apply the
second derivative test.
3. How many liters of water containing 3 grams of salt water per liter must be
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Unformatted text preview: combined with 4 liters of water which contains y grams ( y is less than 2) of salt per liter to yield a solution with 2 grams of salt per liter. 4. Find the linear approximation of f ( x ) = x 2 e 3 x at x = 2. 5. A steel bar is initially at a temperature of 550 ◦ C and cools down according to Newton’s law of cooling. The temperature of the surrounding is 50 ◦ C. Initially the steel bar is cooling at a rate of 20 ◦ C per minute. What was the temperature after 20 minutes?...
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This note was uploaded on 12/27/2011 for the course MATH 5B taught by Professor Rickrugangye during the Fall '07 term at UCSB.
 Fall '07
 RickRugangYe

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