Question Suppose exists, find the limit: (1) (2) Sol. (1) (2) (1) (2) Sol. (1) (2) (1) Suppose exists and then (2) Suppose as then

Question Suppose exists and find the limit The solution is Sol.

Derivatives of logarithmic functions The derivative of is Putting a=e, we obtain

Example Ex. Differentiate Sol.

Question Find if Sol. Since it follows that Thus for all

Example Find if Sol. Since it follows that and by definition, Thus for all x

Question Find if (a) (b) (c) Sol. (a) (b)

The number e as a limit We have known that, if then Thus, which by definition, means Or, equivalently, we have the following important limit

Other forms of the important limit Putting u=1/x, we have More generally, if then

Question Suppose exists and find the limit The solution is Sol. Let then

Question Discuss the differentiability of and find Sol. does not exist

Homework 6 Section 3.6: 46, 49, 50 Section 3.7: 16, 20, 34, 35, 39, 40, 63 Section 3.8: 41, 45, 48