By S. Tan
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Many schools and universities require scholars to take at the very least one math direction, and Calculus I is frequently the selected choice. Calculus necessities For Dummies offers motives of key options for college students who can have taken calculus in highschool and need to study an important options as they apparatus up for a faster-paced collage path.
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What is the F-intercept of the line? What does it represent? 79. Nuclear Plant Utilization The United States is not building many nuclear plants, but the ones that it has are running full tilt. 082 where t is measured in years, with t ϭ 0 corresponding to the beginning of 1990. a. Sketch the line with the given equation. b. What are the slope and the y-intercept of the line found in part (a)? c. Give an interpretation of the slope and the y-intercept of the line found in part (a). d. If the utilization of nuclear power continued to grow at the same rate and the total capacity of nuclear plants in the United States remained constant, by what year were the plants generating at maximum capacity?
Y 0 y x x 0 y 7 6 5 4 3 2 1 Ϫ2Ϫ1 0 1 2 x ϩ1 2 31. f(x) ϭ Ϫ2x ϩ 1 y ϭ f(x) 41. 0 1 2 3 4 5 6 7 8 9 10 x 42. y y x x 0 Ϫ3 a. Find f(7) . b. Find the values of x corresponding to the point(s) on the graph of f located at a height of 5 units above the x-axis. c. Find the point on the x-axis at which the graph of f crosses it. What is f(x) at this point? d. Find the domain and range of f. In Exercises 29–30, determine whether the point lies on the graph of the function. 29. P(3, 3) ; f(x) ϭ 30. P 1 Ϫ3, Ϫ131 2 ; xϩ1 2x 2 ϩ 7 f(t) ϭ 43.
72. A curve in the xy-plane can be simultaneously the graph of a function of x and the graph of a function of y. 3 SELF-CHECK DIAGNOSTIC TEST 1. Given that sec u ϭ 53 and 0 Յ u Ͻ p2 , find tan u. sin 2x 2. Determine whether the function f(x) ϭ is even, odd, or 21 ϩ cos2 x ϩ 1 neither. cot x Ϫ 1 3. Verify the identity ϭ cot x. 1 Ϫ tan x 4. Using the substitution x ϭ a sin u, where a Ͼ 0 and Ϫp2 Յ u Յ p2 , express a 2 Ϫ x 2 in terms of u. 5. Solve the equation cos u Ϫ 2 sin2 u ϩ 1 ϭ 0, where 0 Յ u Ͻ 2p.