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By Dingle R.

ISBN-10: 0122165500

ISBN-13: 9780122165504

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F(x) 1 sin x 2 1 cos 4 f(x) 2 x 4 147. f (x) = 2 – 3 cos(πx – 6) 148. indd 23 1 2 sin 1 x 2 (A) f (x) = 2 sin(2x) (B) f (x) = –2 sin(2x) (C) f (x) = 2 sin(x) (D) f (x) = 2 sin(πx) (E) f(x) 2 sin 2 x 2 4/4/2014 10:14:03 PM 24 Part I: The Questions 150. indd 24 151. (A) f (x) = 2 cos(x) (A) f (x) = 2 cos(2x) + 1 (B) f (x) = 2 cos(2x) (B) f (x) = –2 cos(2x) + 2 (C) f (x) = 2 cos(πx) (C) (D) f (x) = –2 cos(2x) (D) (E) f(x) f (x) = 2 cos(2x) f(x) 2 cos 1 x 2 f (x) = 2 cos(πx) 2 cos 2 x (E) 4/4/2014 10:14:03 PM Chapter 2: Trigonometry Review 152.

320. f(x) 321. f (x) = 4x3 sec x 322. f(x) 323. Assuming that g is a differentiable function, find an expression for the derivative of f (x) = x2g(x). 324. Assuming that g is a differentiable function, find an expression for the derivative of 1 x 2 g( x ) . f(x) x 325. Find (fg)'(3) if f (3) = –2, f '(3) = 4, g(3) = –8, and g '(3) = 7. 326. f (x) = x2 cos x sin x x2 x csc x f (x) = x2 sin x cot x x1 2 f (x) = sec x tan x x cos x f (x) 316. f (x) = 4x csc x 317. Find (fg)'(4) if f (4) = 3, f '(4) = 2, g(4) = –6, and g '(4) = 8.

2 sin2 x + 8 sin x + 5 = 0 164. 7 cos(3x) – 1 = 3 166. indd 28 4/4/2014 10:14:05 PM Chapter 3 Limits and Rates of Change L imits are the foundation of calculus. Being able to work with limits and to understand them conceptually is crucial, because key ideas and definitions in calculus make use of limits. This chapter examines a variety of limit problems and makes the intuitive idea of continuity formal by using limits. Many later problems also involve the use of limits, so although limits may go away for a while during your calculus studies, they’ll return!

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Asymptotic expansions by Dingle R.

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