By Dale Varberg, Edwin Purcell, Steve Rigdon

**Clear and Concise. Varberg specializes in the main serious concepts. **

This well known calculus textual content is still the shortest mainstream calculus e-book on hand – but covers *all* relevant material wanted by way of, and acceptable to, the research of calculus at this level. It's conciseness and readability is helping you concentration on, and understand, critical strategies in calculus with out them getting slowed down and misplaced in over the top and pointless detail. It is exact, with no being excessively rigorous, updated with no being faddish.

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**Additional resources for Calculus (9th Edition) - Instructor's resource manual**

**Sample text**

H( x ) = x + 4; h(– x) = x + 4; even function 26. F (t ) = – t + 3 ; F (– t ) = – –t + 3 ; neither 27. g ( x) = x x ; g (− x ) = − ; neither 2 2 28. G ( x) = 2 x − 1 ; G (− x) = −2 x + 1 ; neither 25. f ( x) = 2 x ; f (– x) = –2 x = 2 x ; even function ⎧1 if t ≤ 0 ⎪ 29. , Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

Sin 3t = sin(2t + t ) = sin 2t cos t + cos 2t sin t = 2sin t cos 2 t + (1 – 2sin 2 t ) sin t = 2sin t (1 – sin 2 t ) + sin t – 2sin 3 t = 2sin t – 2sin 3 t + sin t – 2sin 3 t = 3sin t – 4sin 3 t 55. 85 in. 50. a. b. c. (−∞,16] f Review and Preview Problems g = 16 – x 4 ; domain [–2, 2] g f = ( 16 – x ) 4 = (16 – x) 2 ; domain (−∞,16] (note: the simplification ( 16 – x ) 4 = (16 – x) 2 is only true given the restricted domain) 51. f ( x) = x , g ( x) = 1 + x, h( x) = x 2 , k(x) = sin x, F ( x) = 1 + sin 2 x = f g h k 52.

51. False: If f(x) and g(x) are odd functions, f ( g (− x)) = f(–g(x)) = –f(g(x)), so f(g(x)) is odd. Let x = ε / 2. If ε > 0 , then x > 0 and x < ε . If ab = 0, a or b is 0, so (a, b) lies on the x-axis or the y-axis. If a = b = 0, (a, b) is the origin. −( x 2 + 4 x + 3) ≥ 0 on −3 ≤ x ≤ −1 . y1 = y2 , so ( x1 , y1 ) and ( x2 , y2 ) d = [(a + b) – (a – b)]2 + (a – a) 2 34. False: The equation of a vertical line cannot be written in point-slope form. 35. True: This is the general linear equation.