Math 152: Midterm 1 Fall ’03 Name:.........................................
1. (10 points) Find a formula for the inverse of the function f(x) = 1+2x
3−x.
2. (20 points) Evaluate the limits
(a) lim
x→1
x−1
tan(x−1) (b) lim
x→1(x−1) cot(x−1).
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Guidelines and tips
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
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
The solutions to the math 152: midterm 1 fall ’03 exam. The exam covers topics such as finding formulas for inverse functions, evaluating limits, finding derivatives, and integrating functions. It also includes a bonus question on the hyperbolic tangent inverse function.
Typology: Exams
Pre 2010
1 / 4
This page cannot be seen from the preview
Don't miss anything!
Related documents
Partial preview of the text
Download Math 152: Fall ’03 Midterm 1 Exam and more Exams Calculus in PDF only on Docsity!
Math 152: Midterm 1 Fall ’03 Name:.........................................
- (10 points) Find a formula for the inverse of the function f (x) = 1 + 2x 3 − x
- (20 points) Evaluate the limits
(a) lim x→ 1
x − 1 tan(x − 1) (b) lim x→ 1 (x − 1) cot(x − 1).
- (20 points) Find the derivatives of the following functions.
(a) f (x) = sin−^1
x (b) f (x) = sinh x^2 .
- (20 points) Evaluate the following integrals
(a)
x + 2 x^2 + 4 dx (b)
dx √ 2 − 2 x − x^2
- (Bonus 10 points) Show that tanh−^1 x =
ln
1 + x 1 − x
for − 1 < x < 1.