Download PDF by John Rogawski, Ray Cannon: Calculus Early Transcendentals (for AP)

By John Rogawski, Ray Cannon

ISBN-10: 1429250747

ISBN-13: 9781429250740

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4x + 9y = 3 4. y − 3 = 12 (x − 6) y y if x increases by 3? Perpendicular bisector (5, 4) Q (1, 2) In Exercises 5–8, find the slope of the line. 5. y = 3x + 2 6. y = 3(x − 9) + 2 7. 3x + 4y = 12 8. 3x + 4y = −8 In Exercises 9–20, find the equation of the line with the given description. x FIGURE 11 22. Intercept-Intercept Form Show that if a, b = 0, then the line with x-intercept x = a and y-intercept y = b has equation (Figure 12) x y + =1 a b 9. Slope 3, y-intercept 8 y 10. Slope −2, y-intercept 3 11.

Show that x¯ is greater than or equal to the true weight x. a b a b 32. Show that f (x) is linear of slope m if and only if f (x + h) − f (x) = mh (for all x and h) 33. Find the roots of the quadratic polynomials: (b) x 2 − 2x − 1 (a) 4x 2 − 3x − 1 In Exercises 34–41, complete the square and find the minimum or maximum value of the quadratic function. w1 x w2 x (A) (B) FIGURE 13 34. y = x 2 + 2x + 5 35. y = x 2 − 6x + 9 50. Find numbers x and y with sum 10 and product 24. Hint: Find a quadratic polynomial satisfied by x.

X a x −b (B) Odd function: f (−x) = −f (x) Graph is symmetric about the origin. (C) Neither even nor odd FIGURE 20 E X A M P L E 4 Determine whether the function is even, odd, or neither. (b) g(x) = x −1 (a) f (x) = x 4 (c) h(x) = x 2 + x Solution (a) f (−x) = (−x)4 = x 4 . Thus, f (x) = f (−x) and f (x) is even. (b) g(−x) = (−x)−1 = −x −1 . Thus, g(−x) = −g(x), and g(x) is odd. (c) h(−x) = (−x)2 + (−x) = x 2 − x. We see that h(−x) is not equal to h(x) or to −h(x) = −x 2 − x. Therefore, h(x) is neither even nor odd.

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Calculus Early Transcendentals (for AP) by John Rogawski, Ray Cannon


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