### Create a StudySoup account

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

Already have a StudySoup account? Login here

# Math 129 Midterm 1 Study Guide Math 129

USC

GPA 4.0

### View Full Document

## About this Document

## 61

## 0

## Popular in Calculus II for Engineers and Scientists

## Popular in Math

This 3 page Study Guide was uploaded by Emma Morrissey on Sunday September 25, 2016. The Study Guide belongs to Math 129 at University of Southern California taught by Takahiro Sakai in Fall 2016. Since its upload, it has received 61 views. For similar materials see Calculus II for Engineers and Scientists in Math at University of Southern California.

## Similar to Math 129 at USC

## Reviews for Math 129 Midterm 1 Study Guide

### 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: 09/25/16

Midterm 1 Study Guide ● Inverse functions (One-to-one) ○ A function has an inverse function if it passes the vertical and horizontal line test ○ Domain and range are switched ○ Reflect across y=x ● Differentiation ○ The derivative is the instantaneous slope/ rate of change/change of rate of a function ○ Differentiation rules ○ Use to find extrema ■ Extrema exist where the first derivative is zero ○ Extreme Value Theorem ■ If the function is continuous and differentiable on a closed interval, it has global extrema ○ Fermat Theorem ■ If local extrema and the first derivative at a point x=C exist, then f’(c) = 0 at the extrema ○ Mean Value Theorem ■ See equation ○ Analyze whether the function is increasing/decreasing and concave up/concave down ■ Increasing when f’(x)>0 ■ Decreasing when f’(x)<0 ■ Concave up when f’’(x)>0 ■ Concave down when f’’(x)<0 ● Inverse Trigonometric Functions ○ Trig functions are only one-to-one on certain intervals π π ■ Sin: − ≤2x ≤ 2 ■ Cos: 0 ≤ x ≤ π π π ■ Tan: − ≤2x ≤ 2 ○ Remember that domain and range are switched for inverses ● Integration ○ Compute the area below a function’s curve ○ Integration Rules ○ Methods ■ Integral Approximation ● Riemann Sums (Right Point, Left Point, Mid Point) ● Error Calculations (See equations) ■ U-Substitution ■ Integration By Parts ■ Partial Fractions ○ Special Integral Scenarios ■ Powers of trig functions ■ Square roots in denominator that can be manipulated into trig functions ○ Evaluation Theorem ○ Fundamental Theorem of Calculus ○ Improper Integrals ■ When the function is not continuous or the limits of integration cannot be evaluated ● Set a dummy variable for the integral and take the limit ● If the limit exists, it is convergent at that point ● If the limit does not exist, it is divergent ■ Power Theorem ■ Comparison Test ○ Calculating area between two curves ■ Find the difference ● Hyperbolic Functions ○ Identities ○ Inverses ● L’Hospital’s Rule ○ When your limit produces an indeterminate quotient, you take the derivative of the numerator and denominator until it can be determined ■ Know what is indeterminate ■ Indeterminate product ● Manipulate into quotient ■ Indeterminate difference ● Manipulate into product ■ Indeterminate powers ● Take the natural log then use e^answer MATH 129 Midterm 1 Equations (f(x) •g(x)) ′= f (x)g(x) +f(x)g (x) cos (x) = (12+cos(2x)) MV T : f (c) = f(b−af(a) sin (x) = (1− cos(2x)) 2 (sin (x)) ′= 1 √1−x 2 ∫tan(x)dx = ln|sec(x)| + C (cos (x)) ′= −1 √1−x 2 ∫sec(x)dx = ln|sec(x)+ tan(x)| + C −1 (tan (x)) ′= 1 2 1+x M =NΔx f(x )[ + 1(x )+ ...2+ f(x N ] b f avg = 1 ∫ f(x)dx) b−a a T N Δ2 [ f(x1)+ 2f(x )2+... + 2f(x N−1 ) +f(x )n ] x −x sinh(x) = e −e Approx Error = |approximation − exact| 2 e +e−x k(b−a)3 cosh(x) = 2 Error Trapezoidal ≤ 12n 2 3 cosh(x) ′ = sinh(x) Error Middle ≤ k(b−2) 24n sinh(x) ′= cosh(x) 2 2 cosh (x)− sinh (x) = 1 ∫udv = uv− vdu∫

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

#### "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.