Name_________________________________________Date____________________Class__________
Day #3 Homework
Find the value of each limit. For a limit that does not exist, state why.
1.
3.
lim 3x 2 (2 x  1)
x   12
lim ( x  6)
2
x  2
3
2.
lim x 3  2 x 2  3x  3
x  1
2
4. lim x  5 x  6
x2
x2
( x  4) 2 16
x
x 0
5. lim  2 tan 
6. lim
7. lim x21
2
8. lim x 23 x  2
  6
x 1 x 1
x2
x 4
Daily Lessons and Assessments for AP* Calculus AB, A Complete Course
Mark Sparks 2012
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3
2
9. lim 5 x4  8 x 2
x  0 3 x 16 x
(2  x) 3  8
x
x 0
11. lim
13.
f ( x  h)  f ( x )
if f(x) = 3x2 – 2x
h
h 0
lim
10. lim
x 0
1 1
x2 2
x
( x  h) 2  2( x  h)  3  ( x 2  2 x  3)
h
h 0
12. lim
2 x 2  4 x , x  2

14. lim f ( x) if f ( x)  
x 2
4 sin x , x  2

4

Daily Lessons and Assessments for AP* Calculus AB, A Complete Course
Mark Sparks 2012
 
Page 32
3 
15. lim e x cos x
x 3
17.
lim x  3
x 3
19. lim

x 0
x 3
1 1
x2 2
x
x 3 2
x 1 x 1
16. lim
18.
2x 2 9x 9
x 2 9
x  3 
20.
x  2

2  x,
lim  2
x  2
 x  2 x, x  2
lim
Daily Lessons and Assessments for AP* Calculus AB, A Complete Course
Mark Sparks 2012
Page 33
21. If lim f ( x)  2 and lim g ( x)  4 , find each of the following limits. Show your analysis
x 3
x 3
applying
the properties of limits.
5 f ( x) 
a. lim 


x  3 g ( x ) 
b. lim  f ( x)  2 g ( x)
c. lim
x 3
e. lim 3 f ( x)  g ( x)
g ( x)
x 3 8
d. lim
4 f ( x)
x 3
f. lim 
x  3
x 3
f ( x) g ( x) 
12

22. If lim f ( x)  0 and lim g ( x)  3 , find each of the following limits. Show your analysis applying
x 4
x 4
the properties of limits.
g ( x) 
a. lim 
x  4  f ( x ) 1 
c. lim g ( x)  3
x 4
b. lim xf ( x)
x 4
d. lim g 2 ( x)
x 4
Daily Lessons and Assessments for AP* Calculus AB, A Complete Course
Mark Sparks 2012
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