Jump to content

Page:Elements of the Differential and Integral Calculus - Granville - Revised.djvu/201

From Wikisource
This page needs to be proofread.
By § 112, when .
Since , this gives ; i.e., . Ans.

Illustrative Example 2. Evaluate ; when .

Solution. This function assumes the indeterminate form for .
Let
then when .
By § 113, when x = 0.
By § 111, when .
since , this gives ; i.e. . Ans.

Illustrative Example 3. Evaluate for .

Solution. This function assumes the indeterminate form for .
Let
then when .
By § 113, when .
By § 112, when x = 0.

EXAMPLES

Evaluate the following expressions by differentiation:

1. Ans. 7. Ans.
2.   1. 8.  
3.   1. 9.  
4.   10.  
5.   e. 11.  
6.   12.   1.
  13.