Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Calculus I Exam, MATH 161, Millersville University, November 10, 2006, Exams of Calculus

Millersville University of Pennsylvania (MU)Calculus

A past exam from millersville university's department of mathematics for calculus i (math 161). The exam covers various calculus concepts, including finding horizontal and vertical asymptotes, critical numbers, local extrema, points of inflection, sketching graphs, minimizing the total area of a rectangular printed region, finding limits, and evaluating indefinite integrals. The exam also includes problems on calculating camera angle rates and evaluating definite integrals.

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

koofers-user-tjw
koofers-user-tjw 🇺🇸

9 documents

1 / 7

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Millersville University Name
Department of Mathematics
MATH 161, Calculus I , Test 3
November 10, 2006
Please answer the following questions. Your answers will be evaluated on their correctness,
completeness, and use of mathematical concepts we have covered. Please show all work and
write out your work neatly. Answers without supporting work will receive no credit. The
point values of the problems are listed in parentheses.
1. (4 points each) Consider the function
f(x) = x3−3
400x.
(a) Find the horizontal and vertical asymptotes of the function, if any.
(b) Find the critical numbers of the function (if any) and the intervals where the
function is increasing and decreasing.
pf3
pf4
pf5

Partial preview of the text

Download Calculus I Exam, MATH 161, Millersville University, November 10, 2006 and more Exams Calculus in PDF only on Docsity!

Millersville University Name Department of Mathematics MATH 161, Calculus I , Test 3 November 10, 2006

Please answer the following questions. Your answers will be evaluated on their correctness, completeness, and use of mathematical concepts we have covered. Please show all work and write out your work neatly. Answers without supporting work will receive no credit. The point values of the problems are listed in parentheses.

  1. (4 points each) Consider the function

f (x) = x^3 −

x.

(a) Find the horizontal and vertical asymptotes of the function, if any.

(b) Find the critical numbers of the function (if any) and the intervals where the function is increasing and decreasing.

(c) Find the local extrema of the function, if any. Classify each extremum as a local minimum or local maximum.

(d) Find the points of inflection of the function (if any) and the intervals where the graph of the function is concave up and concave down.

  1. (10 points) An advertisement consists of a rectangular printed region plus 1-inch mar- gins on the sides and 2-inch margins on the top and bottom. The area of the printed region is to be 92 inch^2. Find the dimensions of the printed region that minimize the total area of the advertisement.
  1. (8 points each) Find the exact values of the following limits, if they exist.

(a) lim x→ 1

ex−^1 − 1 x^2 − 1

(b) lim x→ 0 +

(cos x)^1 /x

  1. (10 points) Find the absolute extrema of the function f (x) = x^2 e−^2 x^ on the interval [0, 2]. Classify each extremum as an absolute maximum or absolute minimum.