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
x2
x2
( x 4) 2 16
x
x 0
5. lim 2 tan
6. lim
7. lim x21
2
8. lim x 23 x 2
6
x 1 x 1
x2
x 4
Daily Lessons and Assessments for AP* Calculus AB, A Complete Course
Mark Sparks 2012
Page 31
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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
x2 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
x2 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
Page 34
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