By Colin Adams, Jon Rogawski

The main winning calculus booklet of its new release, Jon Rogawski’s Calculus bargains a terrific stability of formal precision and devoted conceptual concentration, aiding scholars construct robust computational abilities whereas regularly reinforcing the relevance of calculus to their destiny reports and their lives.

Guided by means of new writer Colin Adams, the hot version remains precise to the overdue Jon Rogawski’s clean and powerful procedure, whereas drawing on vast teacher and pupil suggestions, and Adams’ 3 a long time as a calculus instructor and writer of math books for normal audiences.

W. H. Freeman/Macmillan and WebAssign have partnered to convey WebAssign top rate – a accomplished and versatile suite of assets on your calculus direction. Combining the main primary on-line homework platform with the authoritative and interactive content material from the textbook, WebAssign top class extends and complements the study room event for teachers and scholars.

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Additional resources for Calculus: Early Transcendentals (3rd Edition)

Example text

What is the slope of the line y = −4x − 9? 4. Suppose y = 3x + 2. What is 2. Are the lines y = 2x + 1 and y = −2x − 4 perpendicular? 5. What is the minimum of f (x) = (x + 3)2 − 4? 3. When is the line ax + by = c parallel to the y-axis? To the x-axis? 6. What is the result of completing the square for f (x) = x 2 + 1? y if x increases by 3? 18 CHAPTER 1 PRECALCULUS REVIEW Exercises In Exercises 1–4, find the slope, the y-intercept, and the x-intercept of the line with the given equation. 1. y = 3x + 12 2.

19 51. If objects of weights x and w1 are suspended from the balance in Figure 14(A), the cross-beam is horizontal if bx = aw1 . If the lengths a and b are known, we may use this equation to determine an unknown weight x by selecting w1 such that the cross-beam is horizontal. If a and b are not known precisely, we might proceed as follows. First balance x by w1 on the left as in (A). Then switch places and balance x by w2 on the right as in (B). The average x¯ = 12 (w1 + w2 ) gives an estimate for x.

Because the sine function is periodic with period 2π , θ1 θ1 sin θ2 = − sin θ1 ⇔ θ2 = −θ1 + 2π k or θ2 = θ1 + π + 2π k where k is an integer. Taking θ2 = 4x and θ1 = 2x, we see that θ2 = θ1 + π θ2 = −θ1 sin 4x = − sin 2x −sin θ1 θ2 = −θ1 or θ2 = θ1 + π . 5π 3 2π 3 π 0 π 3 −1 4π 3 π 2 3π 2 2π x 3 1 π 2 π −1 2π −1 (A) y = cos x FIGURE 15 5π 3 x= and π , 2 3π 2 over [0, 2π ]. y = cos 2x • Shift to the left π/2 units: y = cos 2 x + Shift left π/2 units π 2 Expand vertically by a factor of 3 y 3 1 π 2π −3 −3 4π , 3 Compress horizontally by a factor of 2: 3 1 π, • y x 2π , 3 Solution The graph is obtained by scaling and shifting the graph of y = cos x in three steps (Figure 15): sin 4x + sin 2x = 0.

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