final_fa03

# final_fa03 - Math 20B Final Exam Fall 2003 • Print Name,...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 20B Final Exam Fall 2003 • Print Name, ID number and Section on your blue book. • BOOKS and CALCULATORS are NOT allowed. Two sheets of NOTES are allowed. • You must show your work to receive credit. 1. (36 pts.) For each of the following integrals, either evaluate the integral or prove that it diverges. (a) integraldisplay e 1 x 3 ln x dx (b) integraldisplay π/ 2 2 + cos x x dx (c) integraldisplay (1 + 2 u ) 10 du (d) integraldisplay 1 / √ 2 x 2 √ 1- x 2 dx (e) integraldisplay 2 1 1 u + u 2 du (f) integraldisplay e t + e t dt 2. (9 pts.) Express the following in the Cartesian form a + bi or the polar form ( r, θ ), as indicated. Do not leave trig functions in your answers. (a) The values of w = 1 + i 1- 3 i and w in Cartesian form. (b) The values of (1- i ) 1 / 3 in polar form. (c) The value of e 2+ πi/ 4 in Cartesian form. 3. (15 pts.) The equation x 4 + y 4 = 1 describes a curve that looks somewhat like a square with rounded corners. Set up integrals for each of the following.square with rounded corners....
View Full Document

## This note was uploaded on 04/29/2010 for the course MATH MATH 20B taught by Professor Takeda during the Spring '07 term at UCSD.

### Page1 / 2

final_fa03 - Math 20B Final Exam Fall 2003 • Print Name,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online