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Unformatted text preview: 0 25. lim x l �3� 12. Sketch the graph of the following function and use it to deter mine the values of a for which lim x l a f � x� exists: 27. lim
x l1 � 2�x
if x � �1
if �1 � x � 1
f � x� � x
� x � 1�2 if x � 1 x�2
x�3 26. 2�x
� x � 1�2 28. lim
�
x l5 29. lim ln� x 2 � 9�
� ex
�x � 5�3 x l� lim� x csc x 32. lim
� x l 2� 13–16 Sketch the graph of an example of a function f that x�2
x�3 30. lim� cot x x l3 31. lim x l �3� xl2 x 2 � 2x
x � 4x � 4
2 satisﬁes all of the given conditions.
13. lim f � x� � 2,
�
xl1 14. lim f � x� � 1,
�
xl0 lim f � x� � 1, x l 2� 15. lim f � x� � 4,
�
xl3 f �3� � 3, f �1� � 1, lim f � x� � �1, lim f � x� � 0, x l 2� f �0� is undeﬁned lim f x� � 2, x l 3� lim f � x� � 3, x l 4� 1
1
and lim 3
x l 1� x � 1
x3 � 1
(a) by evaluating f � x� � 1�� x 3 � 1� for values of x that
approach 1 from the left and from the right,
(b) by reasoning as in Example 9, and
(c) from a graph of f . 33. Determine lim
�
x l1 x l 0� f �2� � 1, f �1� � 2 ; 34. (a) Find the vertical asymptotes of the function lim f � x� � 2, x l �2 f ��2� � 1 16. lim f � x� � 3,
xl1 lim f � x� � �2, x l 1� y�
lim f � x� � �3, x l 4� ; f �4� � �1 17–20 Guess the value o...
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This note was uploaded on 02/04/2014 for the course MATH 160 taught by Professor Staff during the Spring '08 term at Boise State.
 Spring '08
 STAFF
 Calculus

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