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

Math 201 - Second Midterm Exam, October 2008, Exams of Calculus

The second midterm exam for math 201, held on october 2008. The exam covers various topics in calculus, including newton's law of gravitation, rates of change, differentiation, and tangent lines. Students are required to find derivatives, prove differentiation rules, and find equations of tangent lines.

Typology: Exams

Pre 2010

Uploaded on 08/16/2009

koofers-user-yog
koofers-user-yog 🇺🇸

5

(1)

10 documents

1 / 7

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Math 201
21 October 2008
Second Midterm
NAME (Print!):
Check one: (1pm):
(2pm):
Problem Points Score
1 20
2 20
3 30
4 20
5 10
Total 100
pf3
pf4
pf5

Partial preview of the text

Download Math 201 - Second Midterm Exam, October 2008 and more Exams Calculus in PDF only on Docsity!

Math 201

21 October 2008 Second Midterm

NAME (Print!): Check one: (1pm): (2pm):

Problem Points Score

1 20 2 20

3 30

4 20

5 10

Total 100

Problem 1 (20 points): Newton’s Law of Gravitation states that the magnitude F of the force exerted by a body of mass m on a body of mass M is F =

GM m r^2 where G is the gravitational constant and r is the distance between the two bodies. (a) Find dFdr and explain its meaning. What does the minus sign indicate? (b) Suppose that it is known Earth attracts an object with a force that decreases at the rate of 2 N/km when r = 20, 000 km. How fast does this force change when r = 10, 000 km.

Problem 3 (30 points): Find dydx for each of the following: (a) tan(x − y) = (^) 1+yx 2

(b) y = 2^3

x^2

(c) y = xe

x

Problem 4 (20 points): Prove the following differentiation rules: (a) Using the limit definition of the derivative, prove (^) dxd

x = 2 √^1 x.

(b) Show that for any real number n we have (^) dxd xn^ = nxn−^1.

(THIS PAGE INTENTIONALLY BLANK)