New User Special Price Expires in

Let's log you in.

Sign in with Facebook


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


Create a StudySoup account

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

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

MA 161 Final Exam Study Guide

by: Zack Bales

MA 161 Final Exam Study Guide MA 161

Marketplace > Purdue University > MA 161 > MA 161 Final Exam Study Guide
Zack Bales

Preview These Notes for FREE

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

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Covers concepts from semester
Calculus I
Dr. Mummert
Study Guide
Calculus, Purdue
50 ?




Popular in Calculus I

Popular in Department

This 4 page Study Guide was uploaded by Zack Bales on Monday May 2, 2016. The Study Guide belongs to MA 161 at Purdue University taught by Dr. Mummert in Spring 2016. Since its upload, it has received 171 views.

Similar to MA 161 at Purdue


Reviews for MA 161 Final Exam Study Guide


Report this Material


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: 05/02/16
MA 161 Exam Study Guide  Y=f(a)+f’(a)(x-a)  equation of tangent line  lix a f(x)-f(a) / x-a = lih 0 f(a+h)-f(a) / h  If f is differential at a then f is continuous at a  Prevents differentiability o Discontinuity o Sharp corner o Vertical tangent  Power Rule p p-1 o d/dx (x ) = px  Constant multiple rule o d/xx (C *xf(x)) = C * d/dx (f(x))  d/dx (e ) = e  Product Rule o d/dx (f(x) g(x)) = f(x) g’(x) + g(x) f’(x)  Quotient Rule o d/dx (f(x) / g(x)) = f(x) g’(x) - g(x) f’(x) / g(x)2  Chain Rule o d/dx [f(g(x))] = f’(g(x)) * g’(x) o d/dx (g(x) ) = p(g(x)) p-1g’(x)  Implicit Differentiation o d/dx (x +y = 1) o 2x+2yy’=0 o 2yy’= -2x o yy’ = -x o y’ = -x/y  Y as a function of time o y’ = ky o p(t) = p e0 kt  Newtons Law of Cooling o dT/dt = k(T-Ts)  Half Life o K = ln(1/2) / t 1/2  Related Rates 1. Draw Picture 2. Label (variable = changing) 3. Equation 4. Chain rule with respect to time 5. Unknown/plug in   Linear Approx o L(x) ≈ f(a) + f’(a) (x-a) o x = what you want to find o a = known exact  Max and Mins o f’(x) = 0  local max or min o Extreme Value Theorem  If f is continuous on [a,b] then f has a max or min on (a,b) o Mean Value Theorem  f is continuous [a,b]  f is differentiable (a,b)  then there exists a number between a and b where f’(c) = f(b)-f(a) / b-a  Curve Sketching o f’ + - 0 o f inc dec constant o f’’ + - 0 o f’ inc dec const o f conc up conc dwn linear  First Derivative test o Find f’ o Find critical numbers o f’ is either + or – o if f’ – to + f has min o if f’ + to – f has max  Inflection point o Where f’’ sign changes + to – or – to + o f’’ = 0  L’Hospital’s Rule o Indeterminate form (0/0 ꝏ/ꝏ) o Take limit of f’(x)  Optimization o Picture o Variables o Equations o Function of one variable o Calc  Antiderivative o F is antiderivative of f o F’ = f o F’(x) = f(x) + C  Riemann Sum o Approx area of n rectangles   Fundamental Rule of Calculus 1 o  Fundamental Rule of Calculus 2 o  Integration by Substitution 1. Choose inner function 2. Find u’(x)  u’(x) dx 3. Substitute u for x 4. Integrate 5. Replace u with x


Buy Material

Are you sure you want to buy this material for

50 Karma

Buy Material

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

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."

Anthony Lee UC Santa Barbara

"I bought an awesome study guide, which helped me get an A in my Math 34B class this quarter!"

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."

Parker Thompson 500 Startups

"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."

Become an Elite Notetaker and start selling your notes online!

Refund 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


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:

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

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.