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Limits Worksheet 1

1. This document contains two limit worksheets with multiple parts asking to find limits of various functions as x approaches values. 2. The functions include rational expressions, radical expressions, piecewise functions, and trigonometric functions. 3. Limits are to be found as x approaches values from both sides of the value in some cases.

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242 views2 pages

Limits Worksheet 1

1. This document contains two limit worksheets with multiple parts asking to find limits of various functions as x approaches values. 2. The functions include rational expressions, radical expressions, piecewise functions, and trigonometric functions. 3. Limits are to be found as x approaches values from both sides of the value in some cases.

Uploaded by

jessa
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOC, PDF, TXT or read online on Scribd
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AP Calculus AB Name ___________________________

Limits Worksheet #1

Find each limit. Calculators may not be used.

(2 x + 5) �x - 3 � x - 12
1. xlim 2. lim � � 3. lim
� -3 x �5
�x + 5 � x �7

4. lim
x �2
( x-5 ) 5. xlim
� -4
( x + 2) 2 6. lim(
x �0
x 2 - 5 x + 3)

Use the following functions for #’s 7 – 18:


f ( x) = x 2 - 7 g ( x) = x - 5 h( x) = x 2 - 25

7. lim
x �4
f ( x) 8. xlim
� -3
h( x ) 9. lim
x �2
g ( x)

h( x )
10. lim( f og )( x) 11. xlim 12. lim( g oh)( x)
x �5 � -2 g ( x) x �6

13. xlim f ( x ) + h( x ) 14. 3lim g ( x) 15. lim f ( x ) - h( x) + g ( x )


� -1 x �8 x �4

lim f ( x) f (a + h) - f (a) h ( a + m) - h ( a )
x �4
16. 17. lim 18. lim
lim ( g oh)( x) h �0 h m �0 m
x � -2

lim(sec q) lim (sin q ) lim (cot q )


19. q�
p 20. q�
7p 21. q�
4p
2 4 3

lim (cos q ) lim (csc q ) q)


22. q�
5p 23. q�
3p 24. qlim(tan
�p
6 2
x2 - 2 x <1
25. f ( x) = x +1 x �1; x �3
x + 22 x=3

a) sketch a graph of f(x)

b) f (1) = c) f (2) = d) f (3) = e) f (-1) =

f) lim f ( x) = g) xlim f ( x) = h) lim f ( x) = i) xlim f ( x) =


x �1- �1+ x �1 �2 -

j) lim f ( x) = k) xlim f ( x) = l) xlim f ( x) = m) xlim f ( x) =


x �3 �3+ � -2 �0-

sin x x �0
26. f ( x) = x +2 0 < x �3
- x + 10 x > 3
2

a) sketch a graph of f(x)

b) f (0) = c) f (3) = d) f (2) = e) f (7) =

f) xlim f ( x) = g) xlim f ( x) = h) xlim f ( x) = i) xlim f ( x) =


�0+ �0- �3+ �3-

j) lim f ( x) = k) xlim f ( x) = lim o f ( x) =


l) x � m) lim f (x) =
x �5 �1+ -45 x ��

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