Limited time offer 20% OFF StudySoup Subscription details

UMD - MATH 241 - Study Guide - Midterm

Created by: Benjamin Mao Elite Notetaker

> > > > UMD - MATH 241 - Study Guide - Midterm

UMD - MATH 241 - Study Guide - Midterm

School: University of Maryland
Department: Math
Course: Calculus III
Professor: Ebrahimian
Term: Fall 2016
Tags: Calculus
Name: Practice Exam #1 for 9/23 Exam
Description: Math exam practice
Uploaded: 09/19/2016
This preview shows page 1 of a 1 page document. to view the rest of the content
background image Math 241 Sample Exam 1 A - Time: 50 minutes Name: Write your answer for problem 1 on answer sheet 1. 1. Let − u = (1, 2, −1) and − v = (0, 1, −2) and A = (1, −1, 2). 1a. (7 pts) Find a vector that is perpendicular to both − u and − v . Simplify your answer. 1b. (10 pts) Find an equation for the plane perpendicular to − u that passes through A. Simplify your answer. 1c. (10 pts) Find the projection of − u onto − v . Simplify your answer. Write your answer for problem 2 on answer sheet 2. 2. The position of a particle is given by − r (t) where t > 0. We know that − r (1) = (1, −1, 0) and its velocity is given by − v (t) = (t, 1 t , 2). 2a. (7 pts) Find the acceleration of this particle at time t = 5. 2b. (10 pts) Find − r (t). 2c. (10 pts) Find the length of the path traced out by this particle from t = 1 to t = e. Simplify your answer as much as possible. Write your answer for problem 3 on answer sheet 3. 3. Consider the circle in the plane z = −1 centered at (1, 1, −1) whose radius is 1. 3a. (10 pts) Find a parametrization for this circle. 3b. (10 pts) Using part (a) find the unit tangent and unit normal vectors of this curve at point ( 3
2
, 1+ 3 2 , −1). Write your answer for problem 4 on answer sheet 4. 4. Consider the lines ` 1 : x + 1 2 = y − 1 3 = z and ` 2 : x = 2t + 1 y = 3t + 1 z = t − 2 4a. (7 pts) Show that ` 1 and ` 2 are parallel. 4b. (10 pts) Find the distance between ` 1 and ` 2 . 4c. (10 pts) Find an equation for the plane containing both lines.

This is the end of the preview. Please to view the rest of the content
Join more than 18,000+ college students at University of Maryland who use StudySoup to get ahead
1 Pages 15 Views 12 Unlocks
  • Better Grades Guarantee
  • 24/7 Homework help
  • Notes, Study Guides, Flashcards + More!
Join more than 18,000+ college students at University of Maryland who use StudySoup to get ahead
School: University of Maryland
Department: Math
Course: Calculus III
Professor: Ebrahimian
Term: Fall 2016
Tags: Calculus
Name: Practice Exam #1 for 9/23 Exam
Description: Math exam practice
Uploaded: 09/19/2016
1 Pages 15 Views 12 Unlocks
  • Better Grades Guarantee
  • 24/7 Homework help
  • Notes, Study Guides, Flashcards + More!
Join StudySoup for FREE
Get Full Access to UMB - MATH 241 - Study Guide - Midterm
Join with Email
Already have an account? Login here
×
Log in to StudySoup
Get Full Access to UMB - MATH 241 - Study Guide - Midterm

Forgot password? Reset password here

Reset your password

I don't want to reset my password

Need help? Contact support

Need an Account? Is not associated with an account
Sign up
We're here to help

Having trouble accessing your account? Let us help you, contact support at +1(510) 944-1054 or support@studysoup.com

Got it, thanks!
Password Reset Request Sent An email has been sent to the email address associated to your account. Follow the link in the email to reset your password. If you're having trouble finding our email please check your spam folder
Got it, thanks!
Already have an Account? Is already in use
Log in
Incorrect Password The password used to log in with this account is incorrect
Try Again

Forgot password? Reset it here