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MAC 2311/F07/Calculus I
Exam 2 REVIEW/SAMPLE QUESTIONS(SQ)
** To answer all questions in EXAM2, you must need to be the master of everything that I covered in sections 4.14.7, 5.1-5.2.
*** Do all homework problems listed below, read class notes, and quizzes.
4.1 # 6, 8, 12, 14, 16, 18, 22, 24, 26, 32, 34, 35, 40(16, 34, 40)
4.2 # 2, 4, 8, 10, 12, 14, 16, 17, 18, 20, 38, 44, 46, 49, 50, 61
4.3 # 4, 6, 8, 20, 24, 34, 36, 46, 49, 84
4.4 # 4, 6, 14, 16, 20, 24, 28, 34, 38, 40, 44, 50
4.5 # 4, 10, 20, 22, 24, 26, 28, 30, 32, 36, 38, 40, 64, 68
4.6 # 1-4, 5, 8, 10, 12, 18, 21, 28, 30, 39, 44
4.7 # 4, 6, 14, 20, 21, 22, 23, 24
5.1 # 10, 12, 18, 22, 26, 32, 36, 40, 43
5.2 # 4, 8, 11, 16, 24, 28, 48, 52
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2 3 2
t  t  4t  2
3
a) Find critical numbers.
b) Find intervals on which the function is increasing and decreasing.
c) Find intervals on which the function is concave upward and concave downward.
d) Find point of inflection.
e) Find all relative extrema.
f) Sketch the graph of f(t).
SQ1.Let f (t ) 
SQ2. Consider the function f ( x)  x( x 2  x  2), [1,1] . Determine whether the Mean Value Theorem
can be applied to f on the closed interval [ a, b]. If the Mean Value Theorem can be applied , find all
values of c in the open interval such that f ' (c) 
f (b)  f (a )
ba
SQ3. Find the relative extrema:
i) f ( x)  2 x 3  3x 2  12 ii ) f ( x)  x  4
x
SQ4. Find the limit.
a)
lim x (2  5e  x ) b)
d)
lim
x 
lim x
3( x  cos x)
c)
x
lim x ( x  x 2  3 )
2 sin x
x
SQ5. Consider the function f ( x) 
a) Find intercepts;
b) Find asymptotes;
c) Find critical numbers;
d) Find possible point of inflection;
e) Find domain;
2( x 2  9)
(goal: analyze and sketch the graph).
x2  4
2
f) Find axis of symmetry;
g) Find intervals on which the function is increasing or decreasing;
h) Find relative extrema;
i) Find intervals on which function is concave up or down; and
k) Sketch the graph
SQ6. (Maximum volume problem)
a) Verify that each of the rectangular solids shown in the figure below has a surface area of 150 square
inches.
b) Find the volume of each solid.
c) Determine the dimensions of a rectangular solid(with a square base) of maximum volume if its surface
area is 150 square inches.
SQ7. A rectangular page is to contain 24 square inches of print. The margins at the top and bottom of the
1
2
page are to be 1 inches, and the margins on the left and right are to be 1 inch. What should be
dimensions of the page be so that the least amount of the paper will is used?