AP Calculus AB Limits Test: 2010-2011
Name: ______________________________________________
#1.
Use the graph below to answer the questions that follow.
Each part of this problem is worth 2 points!
f (x)
a)
d)
lim f (x) =
b)
lim f (x) =
e)
x!"3"
x!"1"
lim f (x) =
c)
lim f (x) =
f)
x!"3+
x!"1+
lim f (x) =
x!"3
lim f (x) =
x!"1
g)
Is f (x) continuous at x = 1 ? Justify your answer using Calculus.
h)
Is f (x) continuous at x = 3 ? Justify your answer using Calculus.
i)
Is f (x) continuous at x = !1 ? Justify your answer using Calculus.
AP Calculus AB Limits Test: 2010-2011
Name: ______________________________________________
#2.
a)
Use the table below to answer the questions that follow.
Part a is worth 2 points and part b is worth 1 point.
10 x ! 1
Complete the chart below for f (x) =
and c = 0 . Use your graphing
x
calculator with !Tbl = .001 .
c ! .004 c ! .003 c ! .002 c ! .001 c
c + .001 c + .002 c + .003 c + .004
X
Y1
10 x " 1
.
x!0
x
b)
Use the table to determine lim
#3.
Describe in words the difference between the meaning of lim f (x) and f (c) .
x!c
This problem is worth 3 points.
5x
to answer the questions that follow.
x
Each part of this problem is worth 2 points!
#4.
Use the function f (x) =
a)
Write f (x) as a simplified piecewise function.
b)
Sketch the graph of f (x) on the coordinate plane provided.
c)
Determine lim" f (x) .
x!0
d)
Determine lim+ f (x) .
x!0
e)
Determine lim f (x) .
x!0
AP Calculus AB Limits Test: 2010-2011
Name: ______________________________________________
Determine each of the following limits algebraically. You may use your graphing
calculator to check your answers; however, no credit will be given if the correct algebra
is not shown. Each of the following problems are worth 6 points each!
5x 6 # 2x # 1
x!" 3 # 7x 3 # x + 2x 5
#5.
lim
#6.
lim
#7.
lim
#8.
$ x + 1 , if x < 0 '
lim %
(
x!2 cos " x , if x # 0
&
)
#9.
If f (x) = 2x 2 + 1 , then determine lim
#10.
lim
#11.
1
1
"
lim x + 3 3
x!0
x
#12.
lim
#13.
lim"
x 2 + 3x " 40
x!5
2x " 10
x!2
x!0
#15.
f (x) " f (0)
.
x2
sin 5x
x!0
x
x
x! " cos x
x!5
#14.
2x + 5 " x + 7
x"2
3x " 15
5"x
lim ( 2# " 4 )
x!"7
Determine the values of a and b so that f (x) is everywhere continuous. Justify
your answer.
"5bx ! 6a
$
f (x) = #!3b ! 4ax
$5x ! 1
%
, if x < !2 &
$
, if x = !2 '
, if x > !2 $(