Docsity
Log inSign up
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
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 Store documents

The best documents sold by students who completed their studies

Search through all study resources
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

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

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

From our blog

Exams and Study
Go to the blog

Fall '04 MAT 250 Exam 3: Calculus Problems, Exams of Analytical Geometry and Calculus

Murray State UniversityAnalytical Geometry and Calculus

Fall '04 exam questions for mat 250, focusing on calculus concepts such as limits, differentiation, and optimization. Students are required to use l'hospital's rule, find linearizations, estimate roots, determine intervals of increase/decrease, and sketch graphs. Additionally, there are problems on concavity and the mean value theorem.

Typology: Exams

Pre 2010

Uploaded on 08/16/2009

koofers-user-mer-1
koofers-user-mer-1 🇺🇸

10 documents

1 / 4

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Fall ’04/MAT 250/Exam 3 Name: Show all your work.
1. (9pts) Use L’Hospital’s rule to find the limits:
a) lim
x→∞
ln x
√x=
b) lim
x→0(1 + x)−1
x=
2. (6pts) The function f(x) = √xis given.
a) Find the linearization of this function around the point a= 25.
b) Use the linearization to estimate √26. How far is your estimate from √26?
pf3
pf4

Partial preview of the text

Download Fall '04 MAT 250 Exam 3: Calculus Problems and more Exams Analytical Geometry and Calculus in PDF only on Docsity!

Fall ’04/MAT 250/Exam 3 Name: Show all your work.

  1. (9pts) Use L’Hospital’s rule to find the limits:

a) lim x→∞

ln x √ x

b) lim x→ 0 (1 + x)−^ x^1 =

  1. (6pts) The function f (x) =

x is given. a) Find the linearization of this function around the point a = 25. b) Use the linearization to estimate

  1. How far is your estimate from
  1. (10pts) Let f (x) = x^3 + 3x^2 − 24 x + 2. a) Find the intervals of increase/decrease and where f has a local maximum and minimum. b) Find the intervals where f is concave up or down. c) Use your calculator and the results of a) and b) to accurately sketch the graph of f.
  2. (5pts) Suppose that for a continuous and differentiable function f we have − 1 ≤ f ′(x) ≤ 2 for all x in [3, 5] and f (3) = 7. Use the Mean Value Theorem to show that 5 ≤ f (5) ≤ 11.
  1. (8pts) Farmer Tom wants to fence in a rectangular area of 5km^2. What dimensions of the rectangle minimize the cost of the fence? Verify that your dimensions indeed give you a minimal cost.

Bonus. (5pts) Suppose f is a function that is positive (f (x) > 0) and concave up on (− 1 , 1). a) Show that g(x) = [f (x)]^2 is concave up on (− 1 , 1). b) Find a an example of a function f that is concave up, yet negative on (− 1 , 1) for which g = f 2 is concave down. (Hint: think of a simple function!)