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mathematics
college mathematics for business economics

Questions and Answers of College Mathematics For Business Economics

In Problems 61-68, f(x) is continuous on (-∞, ∞ ). Use the given information to sketch the graph of f. f'(x) +++ 0 f(x) 1 -2 1 -0- 1 - 1 3 02 0 2 ➤X 1 1 2 -1
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 1 ex
In Problems 59–66, show that the line y = x is an oblique asymptote for the graph of y = f(x), summarize all pertinent information obtained by applying the graphing strategy, and sketch the graph
In Problems 61-68, f(x) is continuous on (-∞, ∞ ). Use the given information to sketch the graph of f. f'(x) - 0 +++ ND x f(x) T -2 2 1 02 2 1 2 4 0
In Problems 63–66, n is a positive integer. Find each limit. x" n lim x→∞ ln x 00
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 2 - 3e2r
In Problems 61-68, f(x) is continuous on (-∞, ∞ ). Use the given information to sketch the graph of f. f(x) + + + ND + + + 0 x f(x) که یک -2 -1 0 0 2 2 -1 0 + + + 2 3 0 ننا
In Problems 59–66, show that the line y = x is an oblique asymptote for the graph of y = f(x), summarize all pertinent information obtained by applying the graphing strategy, and sketch the graph
The price–demand equation for a GPS device isWhere x is the monthly demand and p is the price in dollars. Find the production level and price per unit that produce the maximum revenue. What is the
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = e0.5x + 4e-0.5x
In Problems 61-68, f(x) is continuous on (-∞, ∞ ). Use the given information to sketch the graph of f. f(-2) ) = 4, f(0) = 0,ƒ(2) = -4; f'(-2) = 0, f'(0) = 0, f'(2) = = 0; f'(x) > 0 on (-∞,
In Problems 59–66, show that the line y = x is an oblique asymptote for the graph of y = f(x), summarize all pertinent information obtained by applying the graphing strategy, and sketch the graph
In Problems 63–66, n is a positive integer. Find each limit. x lim X 15 et
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 2e0.5x + e-0.5x
In Problems 61-68, f(x) is continuous on (-∞, ∞ ). Use the given information to sketch the graph of f. f(-2) = -1, f(0) = 0, f(2) = 1; f'(-2) = 0, f'(2) = 0; f'(x) > 0 on (-∞, -2), (-2, 2), and
In Problems 59–66, show that the line y = x is an oblique asymptote for the graph of y = f(x), summarize all pertinent information obtained by applying the graphing strategy, and sketch the graph
In Problems 67–70, show that the repeated application of L’Hôpital’s rule does not lead to a solution. Then use algebraic manipulation to evaluate each limit. lim 110 V1 + x² X
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = -4 + 2 ln x
In Problems 61-68, f(x) is continuous on (-∞, ∞ ). Use the given information to sketch the graph of f. f(-1) = 2,f(0) = 0,ƒ(1) = -2; f'(-1) = 0, f'(1) = 0, f'(0) is not defined; f' (x) > 0 on
In Problems 67–70, show that the repeated application of L’Hôpital’s rule does not lead to a solution. Then use algebraic manipulation to evaluate each limit. lim x-100 X V4 + x²
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 53 ln x
In Problems 61-68, f(x) is continuous on (-∞, ∞ ). Use the given information to sketch the graph of f. f(-1)=2, f(0) = 0,f(1) = 2; f'(-1) = 0, f'(1) = 0, f'(0) is not defined; f'(x) > 0 on (-∞,
In Problems 67–70, show that the repeated application of L’Hôpital’s rule does not lead to a solution. Then use algebraic manipulation to evaluate each limit. X I + A + այլ
In Problems 67–70, show that the repeated application of L’Hôpital’s rule does not lead to a solution. Then use algebraic manipulation to evaluate each limit. lim X→∞ (x³ + 1)²
In Problems 49–70, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 1 In(x - 3) -
In Problems 67–72, find the absolute maximum and minimum, if either exists, for each function on the indicated intervals. f(x) = x² 18x² + 32 (A) [-4,4] (B) [1,1] (C) [1,3]
In Problems 71-78, summarize all pertinent information obtained by applying the graphing strategy, and sketch the graph of y= f(x). f(x) x³ - 5x² + 6x x²-x-2
In Problems 71-78, summarize all pertinent information obtained by applying the graphing strategy, and sketch the graph of y= f(x). f(x) r3 5r - 5x² - 6x x² + 3x + 2
In Problems 75-82, apply steps 1-3 of the graphing strategy to f(x). Use a graphing calculator to approximate (to two decimal places) x intercepts, critical numbers, and inflection points. Summarize
In Problems 85-90, find the critical numbers, the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. Do not graph. f(x) = 1 + - X + X
In Problems 85-90, find the critical numbers, the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. Do not graph. f(x) = 3 3- 4 2 I X x²
The graph of the total profit P(x) (in dollars) from the sale of x cordless electric screwdrivers is shown in the figure.(A) Write a brief description of the graph of the marginal profit function y =
Problems 9–16 refer to the following graph of y = f(x). v -4 -2 3 2 + H 2 4 -2 -3 Figure for 9-16 نیا X
Find the indicated quantities for f(x) = 3x2 + 2x + 7:(A) The change in y if x changes from 2 to 4 (B) The average rate of change of y with respect to x if x changes from 2 to 4.(C) The slope of the
Use the four-step process to find f′(x) for f(x) = 4x - 5.
In Problems 9–16, use the graph of the function f shown to estimate the indicated limits and function values. f(-0.5) 2 f(x) 4 1 2 + Figure for 9-16 X
In Problems 9–14, find the indicated quantities for y = f (x) = 3x2. Δ.x, Δy, and Δy/ Δx; given xi 1 and x2 = 4
In Problems 4–10, use the graph of f to estimate the indicated limits and function values. 2 f(x) in Figure for 4-10 X
Problems 9–16 refer to the following graph of y = f(x). 3 2 YH -2 -3 نما Figure for 9-16 X
In Problems 9–12, find the marginal cost function.C(x) = 175 + 0.8x
In Problems 9–16, use the graph of the function f shown to estimate the indicated limits and function values. f(-1.5) 2 f(x) 2 Figure for 9-16 ►x
In Problems 9–14, find the indicated quantities for y = f (x) = 3x2 . Ax, Ay, and Ay/Ax; given x₁ 2 and x₂ = 5
Find the indicated derivatives in Problems 9–26. d -3 dx
In Problems 9–12, find the marginal cost function.C(x) = 4,500 + 9.5x
Problems 9–16 refer to the following graph of y = f(x). -4 3 2 + نیا -1 -2 -3 2 Figure for 9-16 4 X
In Problems 9–12, find the marginal cost function.C(x) = 210 + 4.6x - 0.01x2
In Problems 9–16, use the graph of the function f shown to estimate the indicated limits and function values. f(1.75) 2 f(x) 2 Figure for 9-16 ►x
In Problems 9–14, sketch a possible graph of a function that satisfies the given conditions at x = 1 and discuss the continuity of f at x = 1. f(1) = 2 and lim f(x) = -2
Find the indicated derivatives in Problems 9–26. dy dx for y = xº
Problems 9–16 refer to the following graph of y = f(x). v -4 3 2 ترا -1 -2 -3 Figure for 9-16 4 x
In Problems 9–12, find the marginal cost function.C(x) = 790 + 13x - 0.2x2
In Problems 9–16, use the graph of the function f shown to estimate the indicated limits and function values. f(1.25) 2 f(x) 2 Figure for 9-16 ►x
In Problems 9–14, sketch a possible graph of a function that satisfies the given conditions at x = 1 and discuss the continuity of f at x = 1. f(1) = -2 and lim f(x) = −2 -2
Find the indicated derivatives in Problems 9–26. y' for y = x6
In Problems 11–13, use the graph of the function f shown in the figure to answer each question. f(x) 5 5. Figure for 11-13 ·x
Problems 9–16 refer to the following graph of y = f(x). -4 3 2 H 4 -1 -2 -3 Figure for 9-16 2- X
In Problems 9–16, use the graph of the function f shown to estimate the indicated limits and function values. 2 f(x) 2 Figure for 9-16 ►x
In Problems 9–14, find the indicated quantities for y = f (x) = 3x2. Ay/Ax; given X₁ 1 and x₂ = 3
Two hours after the start of a 100-kilometer bicycle race, a cyclist passes the 80-kilometer mark while riding at a velocity of 45 kilometers per hour. (A) Find the cyclist’s average velocity
Find the indicated derivatives in Problems 9–26. dx Х. P
In Problems 14–23, refer to the following graph of y = f(x): 20 10 -2 - 10 2 4 6 Figure for 14-23 ·x
Problems 9–16 refer to the following graph of y = f(x). -4 3 2 -1 -2 -3 2 Figure for 9-16 4 X
Find the indicated derivatives in Problems 9–26. g'(x) for g(x) = x²
In Problems 14–23, refer to the following graph of y = f(x): 20 10 -2 - 10 2 4 6 Figure for 14-23 ·x
Problems 9–16 refer to the following graph of y = f(x). -4 نا 3 2 -1 -2 -3 I Figure for 9-16 X
In Problems 9–16, use the graph of the function f shown to estimate the indicated limits and function values. 2 f(x) + 2 Figure for 9-16 X
In Problems 15–20, find dy for each function. y = 30 + 12x² - +3
Find the indicated derivatives in Problems 9–26. y' for y = x4
In Problems 14–23, refer to the following graph of y = f(x): 20 10 -2 - 10 2 4 6 Figure for 14-23 ·x
In Problems 13–16, find the marginal revenue function.R(x) = x(25 - 0.05x)
Problems 9–16 refer to the following graph of y = f(x). 3 نیا 2 -1 -2 -3 Figure for 9-16 4 *
Find the indicated derivatives in Problems 9–26. dy dx for y = x 8
Problems 15–22 refer to the function f shown in the figure. Use the graph to estimate the indicated function values and limits. f(0.1) 5 f(x) i Figure for 15-22 5 ➤X
In Problems 14–23, refer to the following graph of y = f(x): 20 10 -2 - 10 2 4 6 Figure for 14-23 ·x
In Problems 17–24, use the graph of the function g shown to estimate the indicated limits and function values. g(1.9) 2 g(x) 4 2 2 Figure for 17-24 X
In Problems 15–20, find dy for each function. y = = x²( 1-5)
Find the indicated derivatives in Problems 9–26. g'(x) for g(x) = x8/3
Problems 15–22 refer to the function f shown in the figure. Use the graph to estimate the indicated function values and limits. f(-1.9) 5 f(x) i Figure for 15-22 5 ➤X
In Problems 14–23, refer to the following graph of y = f(x): 20 10 -2 - 10 2 4 6 Figure for 14-23 ·x
In Problems 17–24, use the graph of the function g shown to estimate the indicated limits and function values. g(0.1) 2 g(x) 4 2 2 Figure for 17-24 X
In Problems 15–20, find dy for each function. y = x³ (60-x)
Find the indicated derivatives in Problems 9–26. f'(x) for f(x) = x²/2
Problems 15–22 refer to the function f shown in the figure. Use the graph to estimate the indicated function values and limits. Explain. 5 f(x) 5 Figure for 15-22 in X
Problems 15–22 refer to the function f shown in the figure. Use the graph to estimate the indicated function values and limits. f(-0.9) 5 f(x) i Figure for 15-22 5 ➤X
In Problems 14–23, refer to the following graph of y = f(x): 20 10 -2 - 10 2 4 6 Figure for 14-23 ·x
In Problems 17–24, use the graph of the function g shown to estimate the indicated limits and function values. g(3.5) 2 g(x) 4 2 2 Figure for 17-24 X
In Problems 15–20, find dy for each function. y = 590 Vx
Find the indicated derivatives in Problems 9–26. for v= 10
In Problems 14–23, refer to the following graph of y = f(x): 20 10 -2 - 10 2 4 6 Figure for 14-23 ·x
In Problems 17–24, use the graph of the function g shown to estimate the indicated limits and function values. g(2.5) 2 g(x) 4 2 2 Figure for 17-24 X
In Problems 15–20, find dy for each function. y = 52V У
Find the indicated derivatives in Problems 9–26. y' for y = 1 -12
In Problems 14–23, refer to the following graph of y = f(x):Identify any vertical asymptotes. 20 10 -2 - 10 2 4 6 Figure for 14-23 ·x
Problems 15–22 refer to the function f shown in the figure. Use the graph to estimate the indicated function values and limits. 5 f(x) 5 Figure for 15-22 in X
In Problems 21 and 22, find the indicated quantities for y = f (x) = 3x2 . (A) f(2+ Ax)-f(2) Ax (simplify) (B) What does the quantity in part (A) approach as Ax approaches 0?
Find the indicated derivatives in Problems 9–26. f'(x) for f(x) = 5x²
In Problems 14–23, refer to the following graph of y = f(x):Identify any horizontal asymptotes. 20 -2 10 -10 T 1 1 2 1 4 6 -X
In Problems 17–24, use the graph of the function g shown to estimate the indicated limits and function values. 2 g(x) 2 2 Figure for 17-24 ▶X
In Problems 21 and 22, find the indicated quantities for y = f (x) = 3x2 . f(3 + Ax)-f(3) (A) (simplify) Ax (B) What does the quantity in part (A) approach as Ax approaches 0?
Find the indicated derivatives in Problems 9–26. d dx -(-2x³)

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