practiceFinal1solutions

practiceFinal1solutions - Math 1A, Spring 2008, Wilkening...

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 1A, Spring 2008, Wilkening Sample Final Exam 1 You are allowed one 8 . 5 11 sheet of notes with writing on both sides. This sheet must be turned in with your exam. Calculators are not allowed. 0. (1 point) write your name, section number, and GSIs name on your exam. 1. (3 points) give precise definitions of the following statements: (a) lim x 3- f ( x ) = 17. ( - definition) (b) f ( x ) is continuous at x (c) f ( x ) has an absolute maximum at x over the interval [ a, b ] Answer: (a) For every > 0 there exists a > 0 such that: if 0 < 3- x < then | f ( x )- 17 | < (b) f ( x ) is defined and lim x x f ( x ) = f ( x ) (c) For every x , if a x b then f ( x ) f ( x ) (Assuming that f ( x ) is defined on [ a, b ] and x is in [ a, b ]) 2. (5 points) Evaluate the integral: Z sinh- 1 (4 / 3) e cosh x sinh x dx Answer: u = cosh x , du = sinh x dx , cosh(0) = 1, cosh(sinh- 1 (4 / 3)) = q 1 + sinh 2 (sinh- 1 (4 / 3)) = p 1 + (4 / 3) 2 = p 25 / 9 = 5 / 3 Z sinh- 1 (4 / 3) e cosh x sinh x dx = Z 5 / 3 1 e u du = e u 5 / 3 1 = e 5 / 3- e 3. (6 points) Let f ( x ) = sin x x x 6 = 0 , 1 x = 0 ....
View Full Document

Page1 / 4

practiceFinal1solutions - Math 1A, Spring 2008, Wilkening...

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