### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# DIFFERENTIAL CALCULUS MTH 251H

OSU

GPA 3.79

### View Full Document

## 24

## 0

## Popular in Course

## Popular in Mathematics (M)

This 3 page Class Notes was uploaded by Mrs. Dedric Little on Monday October 19, 2015. The Class Notes belongs to MTH 251H at Oregon State University taught by Staff in Fall. Since its upload, it has received 24 views. For similar materials see /class/224448/mth-251h-oregon-state-university in Mathematics (M) at Oregon State University.

## Reviews for DIFFERENTIAL CALCULUS

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/19/15

Review Exponential and Logarithmic Functions Whose smarter you or your calculator What is a anyway How about loga 90 Your calculator seems to know and so should you Here is a summary of some facts you must have at your nger tips Exponential Functions some things old and some things new A general exponential function has the form fxaquot fooltacltoo where a gt 0 is a xed real number called its base Laws of Exponents for ab gt 0 and ac and y any real numbers 1 axy away axiy 0 aim 7 ay a any 7 an 11 0 1 a i a a i a 7 a abx ambquot lt7 b b a for ac Irrational ln algebra you learned what amquot means for any rational number exponent m n What did you learn Once amquot is de ned for rational exponents some form of a limiting argument that transcends algebra is needed to give meaning to the expression a for 90 an irrational number What is an irrational number One avenue is to use the following de nition De nition For so irrational a lim aT 7 rational 7 41 where the limit is taken through rational numbers 7 that converge to x Properties of a for a gt 1 The function f a has domain the interval 7007 00 has range the interval 0 00 is increasing and continuous a a 00 as so a 00 a a 0 as so a 700 Stop Sketch a graph of a that has these properties Compare with calculator generated graphs for 2quot 7139 and 10quot Logaritth Fix a base a gt 0 Let x be a positive real number You may have learned the following de nition the logarithm of so with base a denoted logaac is the exponent to which a must be raised to equal 90 aloga an This amounts to saying that logax is the inverse function of the exponential functions That is each of these functions reverses the action of the other alogaquot so for any so gt 0 loga a for any real number x Equivalently yaquot ltgt 9010ng The laws of exponents imply the following laws for logarithms Laws of Logaritth for a gt 0 u and 1 any positive real numbers and p any real number ix u loga m loga u logav log 7 logau 7 log L a 7 11 leg up ploga u log 1 0 Properties of logaac for a gt 1 The function f log 90 has domain the interval 0 00 has range the interval 700 00 is increasing and continuous logaac a 700 as so a 0 logaxaoo asxaoo For the record there is a special base 6 an irrational in fact a transcendental number whose decimal expansion begins 6 2718281828459045235360287 that is especially useful in calculus It so useful that the exponential function e is programmed into every scienti c calculator Stay tuned

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "I used the money I made selling my notes & study guides to pay for spring break in Olympia, Washington...which was Sweet!"

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.