2032 - Math 202 Final Exam Spring 2009 Part I Do all parts...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 202 Final Exam Spring, 2009 Part I Do all parts of the following five problems. (1) Compute the derivative dy dx for each of the following (15 points) : (a) y = x x + x 2 ; (b) y = 2 sin( x ) + e 2 ; (c) y = arctan( e √ x ) . (2) Compute each of the following integrals(30 points): (a) Z 2 x + 1 x 2 + 5 x + 6 dx ; (b) Z x 2 p 9- x 2 dx ; (c) Z e x sec 2 ( e x ) dx ; (d) Z 2 1 √ x ln( x ) dx ; (e) Z π/ 4 p sec( x ) tan( x ) dx. (3) Compute each of the following limits (10 points): (a) Lim x → e x- 1- x 1- cos( x ) ; (b) Lim x → sin(3 x ) 1- e 2 x . (4) Compute the area of the entire region between the two curves y = x 3- 3 x 2 +2 x and y = 3( x- 1). While your answer should be numerical, you need not combine the numbers you get. (Hint: It is helpful to sketch the curves.) (8 points). (5) Sketch the curve given by the equation r = 1- sin( θ ) in polar coordinates, labeling the x and y intercepts, and compute the area it encloses. (7 points) 1 Part II Do all parts of three out of the following five problems (10 points...
View Full Document

This note was uploaded on 10/29/2011 for the course MATH Math taught by Professor Ocken during the Spring '11 term at CUNY City.

Page1 / 2

2032 - Math 202 Final Exam Spring 2009 Part I Do all parts...

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

View Full Document Right Arrow Icon
Ask a homework question - tutors are online