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

Math 220 Exam 1 Solutions - Limits, Derivatives, and Functions, Exams of Calculus

University of Illinois - Urbana-ChampaignCalculus

The solutions to exam 1 of math 220 c&m, covering topics such as limits, derivatives, and functions. Students will find answers to problems involving determining limits, finding formulas for lines, calculating growth rates, and applying the limit definition of derivatives.

Typology: Exams

2011/2012

Uploaded on 12/20/2012

thanefowler
thanefowler 🇺🇸

1 document

1 / 7

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Math 220 C&M Exam 1 Oct. 3, 2012
NAME Score /100
1. Determine the limit.
lim
x→∞
3x3+ 9x+ 2
2x3+7+ex
2. (i) Find a formula for the line that goes through the points (2,4) and (3,7).
(ii) What happens to this function every time xincreases by one unit?
(iii) What is the growth rate of this function?
1
pf3
pf4
pf5

Partial preview of the text

Download Math 220 Exam 1 Solutions - Limits, Derivatives, and Functions and more Exams Calculus in PDF only on Docsity!

Math 220 C&M Exam 1 Oct. 3, 2012

NAME Score /

  1. Determine the limit. lim x→∞

3 x^3 + 9x + 2 2 x^3 + 7 + ex

  1. (i) Find a formula for the line that goes through the points (2, 4) and (3, 7).

(ii) What happens to this function every time x increases by one unit?

(iii) What is the growth rate of this function?

  1. Consider the function f (x) = 6x + 8.

(i) Calculate f (x + 1) − f (x).

(ii) Is this growth rate of f (x) variable or constant?

  1. Let g(x) = aerx.

(i) Would you expect the growth rate of g(x) to be constant or variable?

(ii) Would you expect the percent growth rate of g(x) to be constant or variable?

  1. Use the limit definition of the derivative

f ′(x) = lim h→ 0

f (x + h) − f (x) h

to find f ′(x) for f (x) = x^2 + 5x + 1.

  1. Let f (x) = cos(4esin(x (^2) ) ). Find f ′(x). You may use the rules for taking derivatives. You are NOT required to use the limit definition.
  2. Let g(x) = ex(sin x)(x^4 + 5x + 1). Find g′(x). You may use the rules for taking derivatives. You are NOT required to use the limit definition.
  1. Here are the graphs of three functions, p(x), q(x), and r(x).

Determine which of the graphs below is the derivative of each.

  • p′(x) =
  • q′(x) =
  • r′(x) =