1
Sample Exam: Test One (2.1 – 2.5, 4.5)
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to Multiple Choice answers.
Multiple Choice:
(25 points)
1. For which of the following functions f (if any) does
( )
x
1
lim f x
→
fail to exist?
A.
B.
C.
D.
E.
( )
x
1
lim f x
→
exists for all of the functions above.
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2. Find the limit
x
sin x
lim
x
→∞
if it exists and give a reason to support your
answer.
A. Does not exist; Indeterminate form
∞
∞
B.
L
1
=
; Special Limit
C. Does not exist; Oscillating behavior
D.
L
0
=
; Squeeze Theorem
E. Does not exist; Unbounded behavior
3. Find
0
cos
tan
lim
θ
→
, if it exists.
A. 0
B. 1
C.
e
D.
/ 2
π
E. Does not exist
4. Find any x–values at which
( )
2
x
f x
x
2x
=

is not continuous and identify
each discontinuity as removable or nonremovable.
A.
only x
2 (nonremovable)
=
B.
x
0 (nonremovable); x
2 (nonremovable)
=
=
C.
x
0 (removable); x
2 (nonremovable)
=
=
D.
7
4
Free Response
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 Summer '11
 MarioBorha
 Calculus, lim, Mathematical analysis, Limit of a function, limit lim, E. lim f

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