Fundamentals of Differential Equations (9th Edition)
9th Edition
ISBN: 9780321977069
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
Publisher: PEARSON
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In Exercises 7–10, write a formula for ƒ ∘ g ∘ h.
7. ƒ(x) = x + 1, g(x) = 3x, h(x) = 4 - x
8. ƒ(x) = 3x + 4, g(x) = 2x - 1, h(x) = x2
9. ƒ(x) = sqrt(x + 1), g(x) = 1 /(x+4) , h(x) = 1 /x
10. ƒ(x) = x + 2 /(3 - x) , g(x) = x2 /(x2 + 1) , h(x) = sqrt(2 - x)
2.
Let P(t) represent the population of Los Angeles t years after 1900.
(a)
Interpret P(10) = 319, 198 in words.
P(10) - Р(0)
(b)
Given that P(0) = 102, 479 and P(10) = 319, 198, calculate and interpret
10 – 0
in words.
(c)
of Los Angeles reached 200,000.
Set up an equation that could be used to find how many years after 1900 the population
In Problems 47–52, find functions f and g so that f ∘ g = H.
Chapter 6 Solutions
Fundamentals of Differential Equations (9th Edition)
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- In Problems 23–30, use the given zero to find the remaining zeros of each function.arrow_forwardIn Problems 33–44, determine algebraically whether each function is even, odd, or neither. 34. f(x) = 2x* –x? 38. G(x) = Vĩ 33. f(x) = 4x 37. F(x) = V 35. g(x) = -3x² – 5 39. f(x) = x + |x| 36. h (х) — Зx3 + 5 40. f(x) = V2r²+ 1 x² + 3 -x 42. h(x) =- 1 2x 44. F(x) 41. g(x) 43. h(x) x2 - 1 3x2 - 9arrow_forwardFor each of the equations in Exercises 59–62, y is defined as an implicit function of x. Solve for y, and use what you find to sketch a graph of the equation. 59. x² + y = 9 60. (x– 1)2 + (y + 2)² = 4 61. x? – 3y? = 16 62. 4y? — х? + 25 3 0arrow_forward
- 10, 14, 16, Page 52. Find the real and imaginary parts of the following functions: (a) f(z) = −3z + 2z − i; - (b) f(z) = 2 + 1/ z;arrow_forwardIn Problems 13–24, use the graph of the function f given.arrow_forwardIn the section opener, we saw that 80x – 8000 f(x) 30 s xs 100 110 models the government tax revenue, f(x), in tens of billions of dollars, as a function of the tax rate percentage, x. Use this function to solve Exercises 55–58. Round to the nearest ten billion dollars. 55. Find and interpret f(30). Identify the solution as a point on the graph of the function in Figure 6.4 on page 439. 56. Find and interpret f(70). Identify the solution as a point on the graph of the function in Figure 6.4 on page 439. 57. Rewrite the function by using long division to perform (80x - 8000) - (x - 110). Then use this new form of the function to find f(30). Do you obtain the same answer as you did in Exercise 55? Which form of the function do you find easier to use? 58. Rewrite the function by using long division to perform (80x – 8000) - (x – 110).arrow_forward
- 1. In the figure below, find the number(s) "c" that Rolle's Theorem promises (guarantees). 10 For Problems 2–4, verify that the hypotheses of Rolle's Theorem are satisfied for each of the func- tions on the given intervals, and find the value of the number(s) "c" that Rolle's Theorem promises. 2. (a) f(x) = x² on |-2, 2 (b) f(x) = x² =5x +8 on [0,5] 3. (a) f(x) = sin(x) on [0, 7] (b) f(x) = sin(x) on [A,57]| 4. (a) f(x) = r-x+3 on | 1,1] (b) f(x) = x cos(x) on (0, [0, 1arrow_forwardIn Exercises 57–62, find the zeros of ƒ and sketch its graph by plotting points. Use symmetry and increase/decrease information where appropriate. 57. f(x) — х? — 4 58. f(x) = 2x2 – 4 %3D %3D 59. f(x) — х3 — 4х 60. f(x) — х3 61. f(x) =2 – x3 62. f(x) = (x – A)¾i+ate Windarrow_forward3. 4. 5. 6. y(1.5, 5) fy = f(x) (2, 8) Ay = f(x) 6 y= g(x) 3- (-2, 8) 8F (-2, 0) (2, 0) -3 3 71, -3) үз, - 12) Ty= f(x)\ (-1,0). [ (4, 0). (-3, –12), 3 -4 -2 - (1, 2) -12- 4 y = g(x) -4- y= g(x)\ (a) f(x) > 0 (b) f(x) f(x) (b) f(x) >g(x) (a) f(x)arrow_forwardExercises 121–140: (Refer to Examples 12–14.) Complete the following for the given f(x). (a) Find f(x + h). (b) Find the difference quotient of f and simplify. 121. f(x) = 3 122. f(x) = -5 123. f(x) = 2x + 1 124. f(x) = -3x + 4 %3D 125. f(x) = 4x + 3 126. f(x) = 5x – 6 127. f(x) = -6x² - x + 4 128. f(x) = x² + 4x 129. f(x) = 1 – x² 130. f(x) = 3x² 131. f(x) = 132. /(x) 3D글 = = 132. f(: 133. f(x) = 3x² + 1 134. f(x) = x² –- 2 135. f(x) = -x² + 2r 136. f(x) = -4xr² + 1 137. f(x) = 2x - x +1 138. f(x) = x² + 3x - 2 139. f(x) = x' 140. f(x) = 1 – xarrow_forwardIn Problems 49–56, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. Identify any local maximum values or local minimum values.arrow_forwardIn Problems 23–30, use the given zero to find the remaining zeros of each function. 23. f(x) = x - 4x² + 4x – 16; zero: 2i 24. g(x) = x + 3x? + 25x + 75; zero: -5i 25. f(x) = 2x* + 5x + 5x? + 20x – 12; zero: -2i 26. h(x) = 3x4 + 5x + 25x? + 45x – 18; zero: 3i %3D 27. h(x) = x* – 9x + 21x? + 21x – 130; zero: 3 - 2i 29. h(x) = 3x³ + 2x* + 15x³ + 10x2 – 528x – 352; zero: -4i 28. f(x) = x* – 7x + 14x2 – 38x – 60; zero:1 + 3i 30. g(x) = 2x – 3x* – 5x – 15x² – 207x + 108; zero: 3iarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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