Calculus: Early Transcendentals by Michael P. Sullivan

By Michael P. Sullivan

Michael Sullivan and Kathleen Miranda have written a modern calculus textbook that teachers will appreciate and scholars can use. constant in its use of language and notation, Sullivan/Miranda’s Calculus bargains transparent and unique arithmetic at a suitable point of rigor. The authors support scholars research calculus conceptually, whereas additionally emphasizing computational and problem-solving abilities.

The e-book incorporates a wide selection of difficulties together with enticing problem difficulties and utilized routines that version the actual sciences, existence sciences, economics, and different disciplines. Algebra-weak scholars will take advantage of marginal annotations that support increase algebraic realizing, the various references to check fabric, and broad perform routines. powerful media choices contain interactive figures and on-line homework. Sullivan/Miranda’s Calculus has been equipped with today’s teachers and scholars in brain.

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The graph of h is not symmetric with respect to the y-axis and not symmetric with respect to the origin. (d) The domain of F is (−∞, ∞), so for every number x in its domain, −x is also in the domain. Replace x by −x and simplify. F(−x) = |−x| = |−1| · |x| = |x| = F(x) The function F is even. So the graph of F is symmetric with respect to the y-axis. (e) The domain of H is {x|x = 5}. The number x = −5 is in the domain of H , but x = 5 is not in the domain. So the function H is neither even nor odd, and the graph of H is not symmetric with respect to the y-axis or the origin.

To express V as a function of h only, we use the fact that a cross section of the cone and the liquid form two similar triangles. See Figure 34. Corresponding sides of similar triangles are in proportion. 2 • Library of Functions; Mathematical Modeling 21 Then NEED TO REVIEW? 2, pp. A-13 to A-14. V = 1 2 1 πr h = π 3 ↑ 3 r= 1 h 4 2 h= 1 π h3 48 1 h 4 1 π h 3 expresses the volume V as a function of the height of the liquid. 48 Since h is measured in meters, V will be expressed in cubic meters. ■ So V = V (h) = NOW WORK Problem 29.

On what interval(s) is the function f nondecreasing? 13 14 Chapter P • Preparing for Calculus In Problems 55–60, answer the questions about the function 69. 70. x +2 . g(x) = x −6 y 55. What is the domain of g? 1 58. If g(x) = 2, what is x? What is(are) the corresponding point(s) on the graph of g? (1, 0) Ϫ2 57. If x = 4, what is g(x)? What is the corresponding point on the graph of g? 71. y 4 65. Find the average rate of change of f (x) = −2x 2 + 4: (a) From 1 to 2 (b) From 1 to 3 (c) From 1 to 4 (d) From 1 to x, x = 1 Ϫ2 y (2, 1) (2, 1) (0, 0) 2 x Ϫ2 (0, 0) y (Ϫ3, 8) y ϭ x2 Ϫ 1 y ϭ x2 4 y ϭ x3 (1, 1) (Ϫ1, 1) Ϫ2 (2, 8) 8 (0, 0) Ϫ2 2 (1, 0) x Ϫ2 (Ϫ1, 0) Ϫ2 (0, Ϫ1) 2 x 73.

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