Find
SOLUTION: , where f(x) = . The value of the limit is x−1/2
when x = 9, or .
Example 50 __
Find .
SOLUTION: , where f(x) =.
Verify that and compare with Example 17.
Example 51 __
Find .
SOLUTION: , where f (x) = e x. The limit has value e 0 or 1 (see
also Example 41.)
Example 52 __
Find .
SOLUTION: , where f (x) = sin x, because we can write
The answer is 1, since f ′(x) = cos x and f ′(0) = cos 0 = 1. Of course, we already
know that the given limit is the basic trigonometric limit with value 1. Also,
L’Hôpital’s Rule yields 1 as the answer immediately.