Advanced Calculus of a Single Variable by Tunc Geveci

Author:Tunc Geveci
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

Therefore,

Figure 3.21 shows the graph of

The picture is consistent with the fact that . The discontinuity of f at 1 can be removed by declaring that .

Fig. 3.21

Here is an analog of Theorem 1 that is applicable to limits at infinity:

Theorem 2.

Assume that f and g are differentiable on an interval of the form with A > 0 and that if x > A. If and

exists then

Proof.

We will make use of Theorem 1 by the following device: Let us set u = 1∕x, and . Then

We also have

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.