1271practicemidterm2F09 - x = 0 a(15 points If y(0 =-1...

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Math 1271. Lecture 030 Practice Midterm Exam II
There are a total of 100 points on this exam. To get full credit for a problem
you must show the details of your work. Answers unsupported by an argu-
ment will get little credit. No books, notes, calculators, cell phones or other
elecronic devices are allowed. Do all of your calculations on this test paper.
Problem Score
1.
2.
3.
4.
5.
Total:
1

Problem 1 Compute the indicated derivatives of the functions y = f ( x ) . It
is not necessary to simplify.
a. (5 points) f 0 ( x ) where
f ( x ) =
sin(1 - e
x
)
x
.
b.(5 points) y
0
where
y = ( x + 3)
10
( x
2
- 9)
6
( x - 1)
7
.
2

c.(5 points) f 0 ( x ) where
f ( x ) = x arcsin( x ) .
d.(5 points) f (7) ( x ) where
f ( x ) =
1
2 x + 1
.
.
3

Problem 2 (20 points) Sand falling at the rate of 3 ft
3
/ min forms a conical
pile whose radius r always equals twice the height h . Find the rate at which
the height is changing at the instant when the height is 10 feet. Recall that
the volume V of a right circular cone is V =
1
3
πr
2
h .
4

Problem 3 Let y be a function of x such that x 2 y - y 3 = 1 and the deriva-
tives y
0
and y
00
exist at