The Natural Logarithmic Function and Differentiation

# The Natural Logarithmic Function and Differentiation -...

This preview shows pages 1–10. Sign up to view the full content.

The Natural Logarithmic Function and Differentiation Section 5.1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Defn. of the Natural Logarithmic Function 0 , 1 1 x dt t x From the defn., you can see that ln x Is positive for x>1 and negative for
Properties of the Natural Logarithmic Function 1. The domain is (0, ) and the range is (0, ). 2. The function is continuous, increasing, and one-to-one. 3. The graph is concave downward.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
1 2 3 1 y = ln x
Logarithmic Properties 1. ln (1) = 0 2. ln (ab) = ln a + ln b 3. ln (a n ) = n ln a 4. ln = ln a – ln b b a

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Definition of e The letter e

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: denotes the positvie real number such that ln e = = 1 dt t e 1 1 e 2.71828182846 dt t e 1 1 Area = =1 t y 1 = 1 2 3 e is the base for the natural logarithm Because ln e = 1. Derivative of ln function 1. [ ] , 1 = x x x ln dx d [ ] , ' 1 = = u u u dx du u u ln dx d 2. 3. [ ] , ' = u u u u ln dx d Joke Time What do you call a deer with no eyes? I-have-no-eye-deer (I have no idea!) What did the teddy bear say after eating a whole bag of cookies? Im stuffed!...
View Full Document

## The Natural Logarithmic Function and Differentiation -...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online