New PDF release: A First Course in Calculus, 3rd Edition

By Serge Lang

ISBN-10: 0201042231

ISBN-13: 9780201042238

This 5th version of Lang's booklet covers the entire issues ordinarily taught within the first-year calculus series. Divided into 5 components, each one component to a primary path IN CALCULUS comprises examples and purposes in terms of the subject lined. moreover, the rear of the ebook comprises unique options to a great number of the routines, letting them be used as worked-out examples -- one of many major advancements over past versions.

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B)  () = 3 ⇒  ≈ 23, 56 (d) The range of  is −4 ≤  ≤ 4, or [−4 4]. (e)  is increasing on [−4 4], that is, on −4 ≤  ≤ 4. (f)  is odd since its graph is symmetric about the origin. 3.

But () = 32 + 3 + 2 = 3(2 + ) + 2 = 3(2 +  − 1) + 5, so we see that () = 2 +  − 1. 63. We need to examine (−). (−) = ( ◦ )(−) = ((−)) =  (()) [because  is even] Because (−) = (),  is an even function. 4 The Tangent and Velocity Problems 1. (a) Using  (15 250), we construct the following table: slope =     5 (5 694) 694−250 5−15 = − 444 10 = −444 10 (10 444) 444−250 10−15 = − 194 = −388 5 20 (20 111) 111−250 20−15 = − 139 = −278 5 25 (25 28) 28−250 25−15 30 (30 0) 0−250 30−15 (b) Using the values of  that correspond to the points closest to  ( = 10 and  = 20), we have −388 + (−278) = −333 2 = − 222 = −222 10 = − 250 = −166 15 (c) From the graph, we can estimate the slope of the tangent line at  to be 3.

11. (a) If the graph of  is shifted 2 units upward, its equation becomes  =  () + 2. (b) If the graph of  is shifted 2 units downward, its equation becomes  =  () − 2. (c) If the graph of  is shifted 2 units to the right, its equation becomes  =  ( − 2). (d) If the graph of  is shifted 2 units to the left, its equation becomes  =  ( + 2). (e) If the graph of  is reflected about the -axis, its equation becomes  = − (). CHAPTER 1 REVIEW ¤ 45 (f ) If the graph of  is reflected about the -axis, its equation becomes  =  (−).

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A First Course in Calculus, 3rd Edition by Serge Lang


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