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Material Type: Exam; Class: Calculus II; Subject: Math; University: Portland Community College; Term: Spring 2007;
Typology: Exams
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MTH 252 – Practice Test 1
Part A: No Calculator allowed for these questions
5 h t = t + 3 t − 5. Then state all local minimum
and maximum points on h after first performing a first derivative test. Show all relevant work
in a well-organized manner; you need not write any further explanation.
MTH 252 Practice Test 2
3 2 f x = x − 6 x + 9 x + 4 over the interval
you present your work in a manner consistent with that exemplified in lecture.
a. Evaluate
2
2
lim 3 sin
x
x
x
.
1/26/2007 4:52PM
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MTH 252 Practice Test 2
d. Evaluate
0 2
lim x → 1 cos x 1 cos x
.
10/15/2006 3:35PM
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MTH 252 Practice Test 2
explanation so that your reasoning is readily apparent.
A sketch might help your explanation.
t g t t
does not have an absolute maximum value over the interval
. Briefly explain why this does not contradict the absolute maximum/minimum
theorem.
x
y
limit is of indeterminate form.
Table 1: Limits and student answers for problem 3
Limit Form of limit Is limit of indeterminate form?
2
1
lim x → ln
x
x
2
1
lim ln →
x
x
x
ln( )
0
lim 1 →+
x
x
x
x f x x
showing all
relevant work. That’s it – there’s nothing else to be done on this problem.
MTH 252 Practice Test 2
Part B: Use your calculator for all its worth on these problems
x f x x
.
a. What are the critical number(s) of f?
b. Why can you not use a seconds derivative test to determine all of the local minimum and
maximum points on f?
c. State the local extreme points on f after first performing a first derivative test.