133exam2xsolution - Math 133 Dr. Kurtz Exam 2 Name_ Section...

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

View Full Document Right Arrow Icon
Math 133 Exam 2 Name___________________ Dr. Kurtz Section No.______________ TA_____________________ Instructions : Please show all of your work. Credit will not be given for answers with no supporting work. 1. (18 pts) For each rational function, determine the correct form of the partial fractions decomposition, but do not solve for the constants . (a) 52 (2 ) (3 ) 2 3 x AB C xx x x x x =+ + +− + (b) 2 22 2 2 31 (1 ) ( 1 ) 1 ) 1 x xA B C x x x x ++ + + ++++ + D (c) 2 2 2 ) ( 25 ) 1 ( ) B x C D x xxx x 2 E + + + + + 2. (21 pts) Compute dy dx . (a) 1 sin (3 ) x ye = 1 sin 3 2 1 3 1( 3) x dy e dx x ⎛⎞ ⎜⎟ = ⎝⎠ (b) = x y 1 ln tan 1 2 2 11 1 1 1l n y 1 x x x =− ⎛⎞⎜⎟ + Alternatively, 1 tan ( ln ) y x and () 2 n y x x
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) ln(tanh( )) y x = 2 11 sec ( ) tanh( ) 2 yh x x x ⎛⎞ ′ = ⎜⎟ ⎝⎠ 3. (36 pts) Calculate the following integrals. (a) 1 22 1 sec 2 1 2 (2 1) 4 4 1) (2 1) 1 dx dx hx C xx x == −− ∫∫ + (b) 1 0 x x ed x Diff Int 2 2 2 1 2 2 1 2 4 1 0 8 x x x x xe x e e e 1 1 2 2 2 2 2 2 222 0 0 1 1 1 1 4 2 2 4 4 4 4 x x x 2 1 5 x e d x x e x
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

133exam2xsolution - Math 133 Dr. Kurtz Exam 2 Name_ Section...

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