Name _____________________________________________
Date __________________________
AP Calculus Limits Review Worksheet…AWESOME!!!
1. Use the graph at the right to find the following limits.
a.
b.
c.
d.
e.
f.
lim f  x 
________
lim f  x 
________
lim f  x 
________
x  2
x  2
x 2
f  2
________
lim f  x  ________
x 
lim f  x 
x 
________
2. Use the graph at the right to find the following limits.
a.
b.
c.
d.
e.
f.
lim f  x  ________
x 3
lim f  x  ________
x 3
lim f  x 
________
f  3
________
x 3
lim f  x  ________
x 
lim f  x 
x 
________
3. Use the graph at the right to find the following limits.
a.
b.
c.
d.
lim f  x 
________
lim f  x 
________
x  2
x  2
lim f  x  ________
x 
lim f  x 
x 
________
4. Use the graph at the right to find the following limits.
a.
b.
c.
d.
lim f  x 
________
lim f  x 
________
x  2
x  2
lim f  x  ________
x 
lim f  x 
x 
________
5. Use the graph at the right to find the following limits.
a.
b.
c.
d.
lim f  x 
________
lim f  x 
________
x  2
x  2
lim f  x  ________
x 
lim f  x 
________
x 
6. Use the graph at the right to find the following limits.
a.
b.
c.
d.
lim f  x 
________
lim f  x 
________
x  2
x  2
lim f  x  ________
x 
lim f  x 
x 
________
7. Graph the function f  x  
x2
and identify any vertical and horizontal asymptotes.
1  x2
Vertical Asymptotes __________________
8. Graph the function
f  x 
5x
x2  4
and identify any vertical and horizontal asymptotes.
Vertical Asymptotes __________________
9. Find
6 x 4  x 2  1
. __________
x 
2x4  x
lim
1  x3
. __________
x  3 x  2
10. Find lim
Horizontal Asymptotes _______________________
Horizontal Asymptotes _______________________