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2.7 Limits Of Trigonometric Functions

The trigonometric functions have following important limit properties:

Example 1 
 Evaluate   

Solution :  Let L  =   

        

Example 2 Evaluate ( 1 + cot x )

Solution : Let L = ( 1 + cot x )

      = 1 + cot ( p/4 ) = 1 + 1 = 2

Example 3 Evaluate  

Solution : Let L  =  

        

Example 4  Evaluate cot x

Solution : Let L = cot x    =   

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

Solution : Let

L        =  

 

Index

2.1 Modulus
2.2 Inequalities
2.3 Limits Of Functions
2.4 Left Hand And Right Hand Limits
2.5 Theorems On The Algebra Of Limits
2.6 Evaluating Limits
2.7 Limits Of Trigonometric Functions
2.8 The Exponential Limits

Chapter 3





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