Name_____________________________
Honors Calculus Limit Test Review
Solve each problem algebraically. Use proper notation and show all work. You may not
use a calculator for questions 1-20.
1) lim 5x  14
x 2
( x 2  6 x  16)
x 8 ( x 2  11x  24)
3) lim
5) lim
x 
6 x 4  3x 2  2 x
2x 2
7) lim 7  4 x 3
x 
9) lim
x0
2 sin( 3x)
sin( 5 x)
2) lim 5
x 6
4) lim
7
x
6) lim
x3  4
( x  3)( x  2)
x0
x 3
5x 3  2 x  3
x  2 x 3  x 2  1
8) lim
 3x  1 
10) lim sin 

x  
 2x  5 
11) lim x csc x
x 0
x 2
(4  x)( x  2)
x   x 3  3 x  1
13) lim
15) lim cos(
x  
17) lim
x 
1
x 2
12) lim
1
)
x2
1  sin x
2
 ( x  6) ( x  2) ( x  3) 
19) lim 
x 2
5
7 
 2
14) lim sin( x)
x  
2x
x0 sin( 2 x)
16) lim
18) lim
7x  2
6x  3
x 8
20) lim
x 1
x 1
x  x2  x 1
3
x  16  4
x
21) lim
x 0
22) Determine the
 t 3  1, t  1

lim h(t ), where h(t )   1
t 1
 2 (t  1), t  1
3
and
x c
4
Determine limf ( x )  6g ( x )
23) lim 2 x  4 x2  x  1
24) Given that lim f ( x )  
x 
lim g ( x ) 
x c
x c
25) And 27) Determine the four limits
a ) lim f ( x )
x 4
b ) lim f ( x )
x 4
c ) lim f ( x )
x 
d ) lim f ( x )
x  
28)______Given the following
1
2
and lim g ( x)  ,
x c
2
3
–1/3
1/3
–3/4
–3
None of these
lim f ( x)  
x c
a.
b.
c.
d.
e.
find
lim
x c
f ( x)
.
g ( x)
f(x)
2
3
29) Determine the value of c so that f(x) is continuous on the entire real line when
 x  2, x  5
f (x)  
cx  3 x  5
f. 0
g. 6/5
h. 1
i. 5/6
j. None of these
30) g ( x ) 
k.
l.
m.
n.
o.
2x  3
Determine the vertical asymptotes for g(x).
2x 2  x  3
x = -3/2, x = 1
x = -3/2
x=1
y=1
None of these
31) State the conditions needed for a function to be continuous at a point.
32) The cost in millions of dollars for a governmental agency to seize x percent of an
528 x
, 0  x  100
illegal drug is given by the following equation. C 
100  x
a. Find the cost of seizing 25 percent of the drug.
b. Find the cost of seizing 75 percent of the drug.
33) Find the limit of C as x→100- and interpret its meaning.
34) lim
x 1
x2  x  2
x2 1
35) lim 3x  2
x2
41) lim
x 4
sin x
x 0 5 x
42) lim
6  x3
x  7 x 3  3
43) lim
7  6 x5
x  x  8
44) lim
36) lim
37) lim
38) lim
x 
39) lim
x 4
3x 4  x
x2  8
2 x
x  2x  8
cos x tan x
x 0
x
sin 2 x
x 0 3 2
x
2
3x 2  4sin x
x 0
x
45) lim
2 x
x  2x  8
2
46) lim
x 
40) lim
x 4
2 x
x  2x  8
2
2
x 1
x2
47) lim
x 0
x
x
52) lim
x 2
3sin  x 
x 
x
48) lim
x2  x  6
x2
53) Draw a function that has infinite
discontinuities at x = -1 and x = 4.
3x 2  9
x   3  x  3  x 
49) lim
1
1

54) lim x  h x
h 0
h
50) Determine if the function is
 x 2  4, x  2
continuous. g  x   
4, x  2
55) Draw a function that has a jump
discontinuity at x = 3.
56) Draw a function that is continuous
everywhere but at x = 2 (where the
limit does not exist.
51) Determine lim h  x 
x 3
 x  1, x  3
h  x  
 x  5, x  3
57) Draw a function that has a point
discontinuity at x = -1.