2.7 Limits Of Trigonometric Functions
The trigonometric functions have following important limit properties:
![](img15.gif)
Example 1
Evaluate
![](Image564.gif)
Solution : Let L =
![](Image565.gif)
Example 2 Evaluate
( 1 + cot x )
Solution : Let L =
( 1 + cot x )
= 1 + cot ( p/4
) = 1 + 1 = 2 ![](Image567.gif)
Example 3 Evaluate
![](Image569.gif)
Solution : Let L =
![](Image569.gif)
![](Image570.gif)
Example 4 Evaluate
cot x
Solution : Let L =
cot x =
![](Image572.gif)
Here sin x ® 1 and cos x ®
0 as x ® 0 and x > 0 ( in the
1st quadrant). Therefore the function cot x increases without bound
and
cot x = + ¥.
It has a vertical asymptote at x = 0.
Example 5 Evaluate
![](Image574.gif)
Solution : Let
L =
![](Image574.gif)
![](img16.gif)
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