### Create a StudySoup account

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

Already have a StudySoup account? Login here

# 7 Review Sheet for MATH 231 at PSU

### View Full Document

## 26

## 0

## Popular in Course

## Popular in Department

This 3 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Pennsylvania State University taught by a professor in Fall. Since its upload, it has received 26 views.

## Similar to Course at Penn State

## Reviews for 7 Review Sheet for MATH 231 at PSU

### 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: 02/06/15

Math 231 Fall 2008 Review sheet for the nal Exam Our nal exam will cover Chapters 137 147 and 15 This review sheet deals only with Chapter 15 since the midterm review sheet covered the main topics from Chapters 13 and 15 Some important skills 151 152 153 Functions of several variables Finding the domain and the range of a function of two or more variables Sketch the domain of a function of two variables Finding the level curves of a function of two variables Limits and continuity Finding the limit of a function at a point7 provided that it exists or show that the function has no limit at the given point Finding the set of points where a given function is continuous Partial derivatives Finding the rst partial derivatives of a function of two or more variables Finding all second partial derivatives of a function of two or three variables Apply Clairaut7s Theorem7 if it is applicable Finding the indicated higher partial derivatives Tangent planes and linear approximations Finding an equation of the tangent plane to a surface at a given point Finding an equation of the normal line to a surface at a given point Finding the linearization L of a function f at a given point P0 zmyo 20 Use the linearization function at P0 to estimate the value of the function at some point P Finding the total differential of a function 155 The Chain Rule 0 Chain Rule for function of two variables Case 1 0 Chain Rule for function of two variables Case 2 0 Applying the Chain Rule for a function of two or three variables 156 Directional Derivatives and the Gradient Vector o How to nd the directional derivative at a point if the direction is given by a nonunit vector 0 What is the maximum rate of change of a function of two or more variables at a given point 0 Finding the directions in which the directional derivative has a given value 0 Finding the tangent plane and the normal line to a given level surface Fz7 y z k at a given point 157 Maximum and Minimum Values 0 How to nd the critical points of a function of two or three variables 0 How to nd the extreme values local minima and maxima and the saddle points of a function of two or three variables 0 Apply the rst derivative Test for nding critcal points 0 Classify a critical point using the Second derivative test 0 How to nd the absolute minimum and maximum values of ay on a given closed and bounded set 158 Lagrange Multipliers 0 Applying the Method of Lagrange Multipliers for functions of two or three variables subject to one constraint 0 Finding the absolute minimum or maximum values of a function f of two or three variables on the boundary of a given region D in 3 space using the Method of Lagrange Multipliers Other important facts 1 The directional derivative Duf of a function f of three variables at a point P Ly7 z in the direction of a given unit vector u can be written as DufVfu or DuflVflcost97 where 6 is the angle between Vf and u The gradient vector Vf at P gives the direction of most rapidly increase of f at that point The gradient vector Vf at P is normal to the level surface of f passing through P

### 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."

#### "Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

#### "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.