MAT 1235 Calculus II

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

Homework and … • WebAssign HW 6.4* • Quiz 6.3*, 6.4* • Updated schedule (details at the end).

Preview

The Difference…. • Our construction allows us to find the derivatives of (and ). • Compare to the elementary approach (6.2 -6.4), one cannot prove the derivative of .

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

7.3* Property of Inverse Function

So,…

It makes sense to define… Exp. Function with Base

Extended Property of

Law of Exponents

Derivatives and Antiderivatives

Example 1

Example 2

Example 3

Definition: Log. Function with Base a

Derivatives

Example 4

Maple Lab 01 This Friday • You are supposed to know Maple at the level of calculus I. Review tutorials. • Anyone shows up without a working knowledge of Maple will be penalized (quiz at the beginning, not 2014). • All report must be typed with MS Word with equation editor.

Maple and Equation Builder Tool • 2 persons per lab report. • All computations are done on Maple. • All lab reports need to be typed. • Formulas are entered using “Equation Builder Tool” in Word (Window based PC). • It is kind of similar to WebAssign.

Maple • If you are new to Maple, you can learn the basics by doing the Maple tutorials. • You can find them in my Web Pages. • Maple is a very powerful tool. You will use it in other classes in your major.

Maple • You are assumed to know how to use the basics of Maple by next Lab. • I will take points off from you if either you or your partner do not know how to use Maple. • All “new” students should partner with someone who was in 1235 last quarter.

Equation Builder Tool • Follow the handout to practice typing formula.

MAT 1235 Calculus II