131f09x2

# 131f09x2 - 3 5. Calculate: d dx [ sin(tan( x 2 / 3 ) ] = 6....

This preview shows pages 1–8. Sign up to view the full content.

DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS MATH 131, Fall 2009, Exam 2 Your Name: No notes or calculators are permitted on this exam. For questions #1-8, do not simplify your answers. But do use enough parentheses to show clearly how expressions are grouped together. For example write ( x - 1)( x - 2) instead of x + 2 · x - 1. Do all work in the exam booklet and show all necessary steps for full-credit. Turn oﬀ all cellphones, iPods, alarms, etc. Be prepared to show your UMass ID card when you turn in the exam 1: (10 points) 2: (10 points) 3: (10 points) 4: (10 points) 5: (10 points) 6: (10 points) 7: (10 points) 8: (10 points) 9: (10 points) 10: (10 points) TOTAL: (100) 1

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

View Full Document
1. Calculate: d dx ( 6 x + 5 x - x 4 ) = 2. Calculate: d dx [ e - x cos( x 3 + 1) ] = 2
3. Let f ( x ) = ln(3 x - 1). Calculate f 00 ( x ). 4. Calculate: d dx ( (4 x 2 - 1) 2 / 5 1 + sin 2 x ) =

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

View Full Document

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

View Full Document

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: 3 5. Calculate: d dx [ sin(tan( x 2 / 3 ) ] = 6. Calculate f ( z ) where: f ( z ) = ( z 3 + 1 z + cos 2 z ) 2010 4 7. Calculate: d dx [ 2 + arctan(4 x ) ] = 8. Let y satisfy the equation x 2 e y = y 3-1. Then dy dx = 5 9. Find the equation of the tangent line to the curve y = x √ 8-x at the point (4 , 8). 6 10. Let f ( x ) = 2 x 3 + 2 x + 1. Let g ( x ) be the inverse function of f ( x ). This means that f ( g ( x )) = x and g ( f ( x )) = x. (a) Notice that f (-1) =-3 and f (0) = 1 and f (1) = 5. What is g (5)? (2 points) (b) Calculate f ( x ). (3 points) (c) Take the derivative of both sides of f ( g ( x )) = x with respect to x . Now plug in x = 5. Use this to determine g (5). (5 points) 7 This page is for scratchwork 8...
View Full Document

## This note was uploaded on 11/22/2011 for the course MATH 131 taught by Professor Hall-seelig during the Fall '08 term at UMass (Amherst).

### Page1 / 8

131f09x2 - 3 5. Calculate: d dx [ sin(tan( x 2 / 3 ) ] = 6....

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online