Section 6.4* General Log. and Exponential Functions MAT 1235 Calculus II Section 6.4* General Log. and Exponential Functions http://myhome.spu.edu/lauw

Homework and … WebAssign HW 6.4*

Preview

Recall Under our construction, “functions” such as is undefined at this point. We would like to define functions such as so that it is defined for even irrational numbers

Preview Define general exp. and log. function We are going to extend the property of ln⁡(𝑥) to all real numbers 𝑟 (Since 2016) We may skip some of the stories to save time.

6.3* 𝑎>0 Property of Inverse Function

So,…

It makes sense to define… Exp. Function with Base 𝑎>0

Extended Property of ln⁡(𝑥)

Extended Property of ln⁡(𝑥)

Law of Exponents

Law of Exponents

Derivatives and Antiderivatives

𝑎 𝑥 Vs 𝑒 𝑥

Derivatives and Antiderivatives

Example 1

Example 1

Example 2

Example 3

Example 3

Definition: Log. Function with Base a

Derivatives

log 𝑎 𝑥 Vs ln𝑥

Example 4

No Classwork… Y needs to talk about something before the quiz