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

Practice Final Exam - Calculus | MATH 1A, Exams of Calculus

University of California - BerkeleyCalculus
Prof. M. Haiman

Material Type: Exam; Professor: Haiman; Class: Calculus; Subject: Mathematics; University: University of California - Berkeley; Term: Fall 2006;

Typology: Exams

2010/2011

Uploaded on 05/11/2011

koofers-user-v2u
koofers-user-v2u 🇺🇸

5

(1)

9 documents

1 / 6

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Prof. Haiman Math 1A—Calculus Fall, 2006
Final Examination
Name
Student ID
Discussion Section (Time and GSI’s name)
Instructions:
•Do not look at the exam questions before the start of the exam is announced.
•Write your name on each page in case they get separated.
•Write answers in the space provided and turn in only the exam paper. Show enough
work so that we can see how you arrived at your answers.
•You may use one sheet of notes. No other notes, books or calculators allowed.
•The exam has 3 pages (both sides) and 20 questions. All questions have equal value.
Grading use only
1 11
2 12
3 13
4 14
515
6 16
717
8 18
919
10 20
Total:
1
pf3
pf4
pf5

Partial preview of the text

Download Practice Final Exam - Calculus | MATH 1A and more Exams Calculus in PDF only on Docsity!

Prof. Haiman Math 1A—Calculus Fall, 2006 Final Examination

Name Student ID Discussion Section (Time and GSI’s name)

Instructions:

  • Do not look at the exam questions before the start of the exam is announced.
  • Write your name on each page in case they get separated.
  • Write answers in the space provided and turn in only the exam paper. Show enough work so that we can see how you arrived at your answers.
  • You may use one sheet of notes. No other notes, books or calculators allowed.
  • The exam has 3 pages (both sides) and 20 questions. All questions have equal value.

Grading use only 1 11 2 12 3 13 4 14 5 15 6 16 7 17 8 18 9 19 10 20 Total:

  1. Simplify x^1 /^ ln^ x.
  2. If f (x) is continuous on [0, 2], and f (0) = 1, f (1) = 2, f (2) = 0, show that f is not one-to-one.
  3. Find the equation of the tangent line to x^3 + y^3 = 9 at (2, 1).
  4. Evaluate the limit (as a number or an infinite limit):

x→limπ/ 21 cos−^ sin^2 x^ x

  1. Find the point on the line x + 2y = 3 closest to the origin.
  2. Find all local minima and maxima of the function f (x) = x^2 e−x, and the intervals where f is increasing or decreasing.
  3. Show that the equation x^3 − 3 x + 3 = 0 has exactly one real root.
  4. Using Newton’s method to find an approximate solution to the equation x^3 = 2, starting with first approximation x 1 = 1, find the next approximation.
  1. Find f (x) such that f ′′(x) = 1 + sin x, f (0) = 0, and f ′(0) = 0.
  2. Show that ∫^01 e−x^2 dx ≤ (1 + e−^1 /^4 )/2.
  3. Differentiate the function F (x) = ∫^11 /xsin−^1 (t) dt
  4. Evaluate the integral ∫^ −^21 |x^3 | dx.