1232 - Math 202 Part I Final Exam Spring,2008 Do all parts...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 202 Final Exam Spring,2008 Part I Do all parts of the following six problems. (1) Compute the derivative dy dx for each of the following (18 points) : (a) y = 2 arctan(3 x ) ; Ans: y 0 = 3ln(2)2 arctan(3 x ) (1 + 9 x 2 ) . (b) y = x 2 + x x ; Ans: y 0 = 2 x + x x (ln( x ) + 1) . (c) y = ln( q x 4 + 3 x ) . Ans: y 0 = 4 x 3 + 3 2( x 4 + 3) (2) Compute each of the following integrals(24 points): (a) Z x 3 p 4 + x 2 dx ; Ans: with u = 4 + x 2 Z u - 4 2 u du = 1 3 (4 + x 2 ) 3 / 2 - 4(4 + x 2 ) 1 / 2 + C Alternatively, use x = 2tan( t ) , q 4 + x 2 = 2sec( t ) . (b) Z x 3 - 1 x 3 + x dx Ans: Z 1 + - 1 x + x - 1 x 2 + 1 dx = x - ln( x ) + 1 2 ln( x 2 + 1) - arctan( x ) + C. 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
(c) Z cos 3 ( x ) dx ; Ans: let u = sin( x ) , Z (1 - u 2 ) du = sin( x ) - 1 3 sin 3 ( x ) + C. (d) Z 1 0 x ln( x + 1) dx. Ans: let z = x + 1 ,u = ln( z ) ,dv = ( z - 1) dz Z 2 1 ( z - 1)ln( z ) dz = [ 1 2 z 2 - z ]ln( z ) - [ 1 4 z 2 - z ] | 2 1 = 1 4 . (3) Compute each of the following limits (10 points):
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 4

1232 - Math 202 Part I Final Exam Spring,2008 Do all parts...

This preview shows document pages 1 - 3. Sign up to view the full document.

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