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Math 200
Name:
Test #1 Form A
.
1. For the function f whose graph is given, find the following. (20 pts)
a. lim f ( x) =
.
x →
b. lim f ( x) =
.
.
x →−
c. lim+ f ( x ) =
.
d. lim+ f ( x) =
e. lim f ( x ) =
.
f. lim f ( x ) =
x →−1
x →0
x→2
g. lim f ( x) =
.
x→2
.
x →1
h. Vertical asymptote(s) is /are
i. Horizontal asymptote(s) is/are
.
.
j. Is f ( x ) continuous at x = 2 ? Explain your reasoning.
2. Which of the following statements are true, and which are false? Put answer in the answer
blank provided below.(12pts)
e x
if x 0
a. lim+ f ( x) = 1 , if f ( x) =
x →0
ln x if x 0
e x
if x 0
lim
f
(
x
)
=
1
f
(
x
)
=
b.
,
if
x → 0−
ln x if x 0
f ( x)
c. If lim f ( x) = 0 and lim g ( x) = 0 , then lim
does not exist.
x →c
x →c
x →c g ( x )
d. If f ( x ) is undefined at x = c , then the limit of f ( x ) as x approaches c does not exist.
e. If f (c ) = L , then lim f ( x) = L.
x →c
f. If f ( x) = sin x , then lim+ f ( x) =
x→
Form A
2
In Exercises 3-6 circle the best answer. (16pts)
3. If f ( x) = x 2 − 9 , then what is lim ( f ( x) + x ) ?
x →−2
a. −7
b. −3
c. 3
d. 7
e. The limit does not exist.
x2 − 1
if x 1
4. Let f ( x ) = x − 1
Which of the following statements, I, II, III, are true?
2
if x = 1
I. lim f ( x) exists.
x →1
a. only I
b. only II
II. f (1) exists.
c. I and III
d. I, II and III
5. Find value(s) of x at which the function f ( x) =
a.
x = 2
b. x = −2
6. Given the function f ( x) =
a.) y = 0
c. x = 2
III. f ( x ) is continuous at x = 1
e. I and II
( x − 2)2
has a vertical asymptote when,
x2 − 4
d. x = 0
e. none of these
10 x3
, f ( x ) has a horizontal asymptote when
2 x2 − 6
b.) y = 5
7. A line x = −10 is a
if
c.) y = 10
d.) y = 2
e.) Does not exist
asymptote for the graph of a function f ( x) ,
. (6pts)
8. Sketch a possible graph of a function f ( x) , with asymptotes, satisfying all the following
conditions. (6pts)
f (−2) = −1, f (0) = 0, f (2) = 1, f (4) = −1,
lim− f ( x) = , lim+ f ( x) = −, lim f ( x) = −2,
x→3
Form A
x→3
x→−
f (6) = 3,
lim f ( x) = ,
x→
9. Find the exact value of each limit by algebraic methods. Do not give any decimal
approximation (30 pts)
Credit will only be given for work shown.
4( x − 6) x + 10
a. lim
x →6
4 − x + 10
b.
1
1
−
lim 2 + sin x 2
x →0
sin x
c.
x3 − 8
lim 2
x →2 x − 4
d.
x4 − x2 + x + 6
lim
x→−
3x5 − x + 5
e.
lim
x→−
5 − 2x
8 x 2 − 3x
10. Find the intervals on which the function
x3 − 9 x 2
h( x ) = 3
x − 5x2 + 6 x
Credit will only be given for work shown.
11. Find all the asymptotes of g ( x) =
x3 − 27
. (6 pts)
2 x3 − 18 x
Credit will only be given for work shown.
Form A
is continuous. (6 pts)
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