131f08x1ANS - Math 131 Exam 1 Solutions 10/1/08 1. (a) [8%]...

Info iconThis preview shows pages 1–3. 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 131 Exam 1 Solutions 10/1/08 1. (a) [8%] avg v = h (5 . 2) h (5) 5 . 2 5 = [1200 4 . 9(5 . 2) 2 ] [1200 4 . 9(5) 2 ] . 2 = 4 . 9[(5 . 2) 2 + (5) 2 ] . 2 = 4 . 9 2 . 04 . 2 = 49 . 98 m/s . (b) [8%] avg v = h (5 + t ) h (5) t = [1200 4 . 9(5 + t ) 2 ] [1200 4 . 9(5) 2 ] t (m/sec) The question did not ask you to simplify the result, but if you do so, you should obtain: = 4 . 9 ( 25 + 10 t + ( t ) 2 ) + 4 . 9(25) t = 4 . 9(10 t + ( t ) 2 t = 4 . 9 t (10 + t ) t = 4 . 9(10 + t ) (m/sec) 2. (a) [10%] The desired slope m is given by: m = lim h f (4 + h ) f (4) h = lim h [(4 + h ) 2 3(4 + h )] [4 2 3(4)] h = lim h 16 + 8 h + h 2 12 3 h 16 + 12 h = lim h 5 h + h 2 h = lim h h (5 + h ) h = lim h (5 + h ) = 5 + 0 = 5 . (b) [6%] The form of the tangent line is y f (4) = m ( x 4) . The tangent line has slope m = 5 and goes through the point ( 4 , f (4) ) = ( 4 , 4 2 3(4) ) = (4 , 4) . So its equation is y 4 = 5( x 4) , That form is OK. So is a simplified form such as: y = 5 x 16 1 3. (a) [8%] Factor the denominator to obtain f ( x ) = 4 x 2 + 5 ( x 1) ( x 5) ....
View Full Document

Page1 / 4

131f08x1ANS - Math 131 Exam 1 Solutions 10/1/08 1. (a) [8%]...

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