By Michael P. Sullivan
Michael Sullivan and Kathleen Miranda have written a latest calculus textbook that teachers will appreciate and scholars can use. constant in its use of language and notation, Sullivan/Miranda’s Calculus deals transparent and targeted arithmetic at a suitable point of rigor. The authors support scholars research calculus conceptually, whereas additionally emphasizing computational and problem-solving talents.
The e-book encompasses a good selection of difficulties together with enticing problem difficulties and utilized workouts that version the actual sciences, existence sciences, economics, and different disciplines. Algebra-weak scholars will take advantage of marginal annotations that support advance algebraic figuring out, the various references to study fabric, and huge 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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Additional info for Calculus: Early Transcendentals
2 Ϫ2 41. For what values of x is f (x) > 0? 1 Ϫ2 Ϫ2 4 x 52. On what interval(s) is the function f constant? 53. On what interval(s) is the function f nonincreasing? 54. 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)?
F (x) = x = smallest integer greater than or equal to x The domain of the ceiling function x is the set of all real numbers; the range is the set of integers. The y-intercept of x is 0, and the x-intercepts are the numbers in the interval (−1, 0]. The ceiling function is constant on every interval of the form (k, k + 1], where k is an integer, and is nondecreasing on its domain. See Figure 28. y (3, 3) (2, 2) 2 (1, 1) 2 Ϫ2 x <0 The domain of the floor function x is the set of all real numbers; the range is the set of all integers.
DEFINITION Polynomial Function A polynomial function is a function of the form f (x) = an x n + an−1 x n−1 + · · · + a1 x + a0 where an , an−1 , . . , a1 , a0 are real numbers and n is a nonnegative integer. The domain of a polynomial function is the set of all real numbers. 18 Chapter P • Preparing for Calculus If an = 0, then an is called the leading coefficient of f , and the polynomial has degree n. The constant function f (x) = A, where A = 0, is a polynomial function of degree 0. The constant function f (x) = 0 is the zero polynomial function and has no degree.