×

### Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

or

by: Rachel Klein

395

1

2

# Chapter 7 Exam Study Guide MATH 125 010

Rachel Klein
UT
GPA 3.94

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

This is an easy-to-read and fully inclusive of everything you need to know for the Chapter 7 Exam. I have uploaded notes that are more detailed and include examples and detailed definitions.
COURSE
Basic Calculus 125
PROF.
TYPE
Study Guide
PAGES
2
WORDS
CONCEPTS
math 125, Math, Calculus
KARMA
50 ?

## Popular in Math

This 2 page Study Guide was uploaded by Rachel Klein on Thursday February 4, 2016. The Study Guide belongs to MATH 125 010 at University of Tennessee - Knoxville taught by in Spring 2016. Since its upload, it has received 395 views. For similar materials see Basic Calculus 125 in Math at University of Tennessee - Knoxville.

×

## Reviews for Chapter 7 Exam Study Guide

×

×

### What is Karma?

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

Date Created: 02/04/16
Chapter 7 Exam Math 125, Spring 2016 1.! Limits a.! Looks at how a function is behaving as a function approaches a certain point b.! Rules for basic limits !! lim " cb = 0 !! lim " cx = c !! lim x cx = c n " !! lim " ! = " # If n is even, c is positive. If n is odd, c is negative. " c c.! The limit does not exist if there are 2 ways to approach the limit !! However, it can have a limit from the left and a limit from the right d.! Properties of Basic Limits !! lim " cf(x) = L !! lim x cg(x) = K " •! lim (b(f(x)) = bL " c •! lim " c(f(x) + g(x)) = L + K •! lim " c(f(x)g(x)) = LK •! lim \$(&)= ) " c((&) * •! lim x c(f(x) ) = L " " " •! lim " c +(!) = , 2.! Continuity a.! A function is continuous at a point c when the following are true !! F(c) is defined !! lim " cf(x) exists !! lim x cf(x) = f(c) " b.! Polynomials are always continuous c.! A rational function is continuous at every point on its domain (when x is defined) d.! Removable discontinuity is possible !! You can “make” a function continuous if it can be simplified to a form in which it has an unlimited domain e.! You can have a closed interval [a,b] in which a function is continuous just in this range 3.! Derivatives a.! -.= lim \$ &/0 1\$(&) -& x"h 0 b.! How to find tangent line of a point (a,b) -. !! Find -& -. !! Plug a into ; this value is the slope the tangent line, m -& !! Use point slope formula: y-b = m(x-a) !! Simplify c.! Relationship between differentiable and continuous !! Differentiable " continuous !! NOT continuous " NOT differentiable 4.! Differentiation Rules; “Shortcuts” a.! The Constant Rule: f(x) = c, f’(x) = 0 b.! The Simple Power Rule: f(x) = x , f;(x) = nx n-1 c.! The Constant Multiple Rule: f(x) = c(f(x)), f’(x) = c(f’(x)) d.! The Sum (and difference) Rule: f(x) = f(x) + g(x), f’(x) = f’(x) + g’(x) 5.! Rates of Change ∆. \$ 3 1\$(4) a.! Average Rate of Change between points a and b: ∆& = 314 b.! Average Velocity = 56789:;<8;=<>?785: 56789:;<8;?<@: c.! Instantaneous Rate of Change is the same thing as finding the derivative d.! Marginals are rates of change in economics !! Profit = revenue – cost !! Marginals show an estimate of how much profit/revenue/cost would increase or decrease if x increases by 1 •! The derivative of profit is marginal profit •! The derivative of revenue is marginal revenue •! The derivative of cost is marginal cost e.! The Demand Function !! Demand- the number of goods that customers are willing to buy !! Demand function- the relationship between demand and price, P=f(x) !! Revenue: R(x) = xp = xf(x)

×

×

### BOOM! Enjoy Your Free Notes!

×

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

Jim McGreen Ohio University

#### "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."

Amaris Trozzo George Washington University

#### "I made \$350 in just two days after posting my first study guide."

Steve Martinelli UC Los Angeles

Forbes

#### "Their 'Elite Notetakers' are making over \$1,200/month in sales by creating high quality content that helps their classmates in a time of need."

Become an Elite Notetaker and start selling your notes online!
×

### 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