Analysis and Approaches for IBDP Maths Ebook 2 | Page 204

Your Practice Set – Analysis and Approaches for IBDP Mathematics
62
Paper 1 Section A – L’Hôpital's Rule
Example
Use L’Hôpital's rule to evaluate
x
3
lim
x�0
tan
� 2x
.
x
[5]
Solution
3 2
x �2x 3x
�2(1) � 0 �
lim � lim
x 0 0
2 � �
M1A2
� tan x x�
sec x � 0 �
3 2
x �2x 3x
�2
lim � lim
x�0 0
2
tan x x�
sec x
x
�2x
3(0) �2
� M1
3 2
lim
x�0
tan sec
2
x 0
x
� 2x
2
3
lim �
x�0
tan x 1
3
x � 2x
lim � 2
A1
x�0
tan x
[5]
Exercise 62
1. Use L’Hôpital's rule to evaluate
�
sin x 4
lim
x 0 ln( x 1)
� � . [5]
2. Use L’Hôpital's rule to evaluate
3. Use L’Hôpital's rule to evaluate
4. Use L’Hôpital's rule to evaluate
x
3 � 1 .
x
lim
x�0
sin 2
lim
x�0
cos 2
2
x
.
x�
cos x
1�sec
x
.
x x x
lim
x�0
sin 2 � cos 2 � 1 � 2
[5]
[7]
[7]
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