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 =
