Math_137_Winter_2010_Solution_2

Math_137_Winter_2010_Solution_2 - Math 137 Winter 2010 Text...

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

View Full Document Right Arrow Icon
Math 137 Winter 2010 Assignment 2 Due Friday, January 22 Text problems: Section 1.3: 22. 48. 8 | | 2 ) ( x x H + = One possible decomposition of H(x) into three functions is f ° g ° h where f(x) = 8 x, g(x) = 2 + x, and h(x) = | x |. Section 1.5: 18. Section 1.6: 18. a) f passes the Horizontal Line Test, so f is 1-1. b) Dom f –1 = Ran f = [–1, 3] and Ran f –1 = Dom f = [ –3, 3] c) f –1 (2) is the value x such that f(x) = 2, which means x = 0 d) f –1 (0) –1.6 26. Let x x e e y 2 1 + = . Then y(1 + 2e x ) = y + 2ye x = e x y = e x – 2ye x = e x (1 – 2y) e x = y /(1 – 2y) x = ln(y /(1 – 2y)). So ) 2 1 ln( ) ( 1 x x x f = . 50.
Background image of page 1

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

View Full DocumentRight Arrow Icon
Appendix D: 46. Prove the identity (sin x + cos x) 2 = 1 + sin 2x (sin x + cos x) 2 = sin 2 x + 2 sin x cos x + cos 2 x = sin 2 x + cos 2 x + 2 sin x cos x = 1 + sin 2x = 1 + 2 sin x cos x = 1 + sin 2x 68. Find all values of x in the interval [0,2 π ] that satisfy the equation |tan x| = 1. |tan x| = 1 tan x = 1 or – 1 tan x = 1 x = π /4 or 5 π /4 tan x = –1 x = 3 π /4 or 7 π /4 72. Find all values of x in the interval [0,2 π ] that satisfy the equation 2 + cos 2x = 3 cos x. 2 + cos 2x = 3 cos x 2 + 2 cos 2 x – 1 – 3 cos x = 0 2 cos 2 x – 3 cos x + 1 = 0 Let y = cos x; we have 2y 2 – 3y + 1 = (2y – 1)(y – 1) = 0, for which the solutions are y = 1 or ½ . Hence cos x = 1 or ½ , so x = 0, 2 π , π /3, 5 π /3. Non-text problems: 1. Sketch each of the given functions using graphical operations on basic functions. List the steps you use to obtain the final graph; use two sketches if needed for clarity. a)
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.

This note was uploaded on 02/21/2010 for the course MATH 137 taught by Professor Speziale during the Spring '08 term at Waterloo.

Page1 / 7

Math_137_Winter_2010_Solution_2 - Math 137 Winter 2010 Text...

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