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mathematics
college mathematics for business economics

Questions and Answers of College Mathematics For Business Economics

In Problems 14–23, refer to the following graph of y = f(x):Where is y = f(x) discontinuous? 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. 2 g(x) 2 2 Figure for 17-24 ▶X
Problems 23–30 refer to the function g shown in the figure. Use the graph to estimate the indicated function values and limits. g(-3.1) g(x) 5 Figure for 23-30 HAT
In Problems 23–26, find dy for each function. y = (2x + 1)²
Find the indicated derivatives in Problems 9–26. y' for y = 0.4x7
In Problems 14–23, refer to the following graph of y = f(x):Use the four-step process to find f'(x) for f(x) = 5x2. 20 10 -2 - 10 2 4 6 Figure for 14-23 ·x
Problems 23–30 refer to the function g shown in the figure. Use the graph to estimate the indicated function values and limits.g(-2.1) g(x) 5 in Figure for 23-30 X
In Problems 23–26, find dy for each function. y = (3x + 5)²
Find the indicated derivatives in Problems 9–26. f'(x) for f(x) = 0.8x4
Problems 23–30 refer to the function g shown in the figure. Use the graph to estimate the indicated function values and limits.g(1.9) g(x) 5 -5 Figure for 23-30
In Problems 25–28, use the graph of the function f shown to estimate the indicated limits and function values. 5 f(x) 5 -5 Figure for 25-28 LA X
In Problems 23–26, find dy for each function. y 6+zx X
In Problems 26-31, find f'(x) and simplify. f(x) = ½x² − 5x² + 1 - 3
In Problems 19-42, use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3).f(x) = x2 + 6x - 10
Problems 23–30 refer to the function g shown in the figure. Use the graph to estimate the indicated function values and limits.g(-1.9) g(x) 5 Figure for 23-30 X
Find the indicated derivatives in Problems 9–26. dy dx for y= 25
In Problems 26-31, find f'(x) and simplify. f(x) = 2x1/2 - 3x
Problems 23–30 refer to the function g shown in the figure. Use the graph to estimate the indicated function values and limits.Explain. g(x) 5 Figure for 23-30 ILA X
Problems 23–30 refer to the function g shown in the figure. Use the graph to estimate the indicated function values and limits. g(x) 9 -5 Figure for 23-30 x
In Problems 19-42, use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3).f(x) = 2x2 - 7x + 3
In Problems 25–28, use the graph of the function f shown to estimate the indicated limits and function values. 5 f(x) 5 -5 Figure for 25-28 LA X
In Problems 26-31, find f'(x) and simplify.f(x) = 5
In Problems 26-31, find f'(x) and simplify. f(x) = 3 5x³ + 2x 4
In Problems 29–32, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If a cost function is linear, then the marginal cost is a
In Problems 19-42, use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3).f(x) = -x2 + 4x - 9
In Problems 26-31, find f'(x) and simplify. f(x) = 0.5 x4 X +0.25x4
In Problems 29–32, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If a price–demand equation is linear, then the marginal
In Problems 29–38, find each limit if it exists. lim 3x x-2
In Problems 19-42, use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3).f(x) = -x2 + 9x - 2
In Problems 29–38, find each limit if it exists. lim (x + 5)
In Problems 19-42, use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3).f(x) = 2x3 + 1
A cube with 10-inch sides is covered with a coat of fiberglass 0.2 inch thick. Use differentials to estimate the volume of the fiberglass shell.
In Problems 32–35, find the indicated quantities for y = f(x) = 2x2 + 5x. Ax, Ay, and Ay/Ax for x₁ 2 and x₂ = 5.
In Problems 29–32, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.Marginal average cost is equal to average marginal cost.
In Problems 29–38, find each limit if it exists. lim (x - 3) x-5
In Problems 19-42, use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x) = 4 + 4 X
In Problems 32–35, find the indicated quantities for y = f(x) = 2x2 + 5x. [f(x₁ + Ax) f(x₁)]/Ax for x₁ = 2 and Ax = 3. -
Find the indicated derivatives in Problems 33–56. d dx -(2x - 5)
In Problems 29–38, find each limit if it exists. lim x(x-4)
In Problems 33–42, use - ∞ or ∞ where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes. f(x) = 1 x + 3
Find the indicated derivatives in Problems 33–56. d dx (-4x + 9)
In Problems 19-42, use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x) 6 = - 2 X
In Problems 32–35, find the indicated quantities for y = f(x) = 2x2 + 5x. dy for x₁ = 2 and x₂ = 5.
In Problems 29–38, find each limit if it exists. lim x(x + 3) x-1
Find the indicated derivatives in Problems 33–56. f'(t) if f(t) = 21² - 3t+1
The total cost (in dollars) of manufacturing x auto body frames is C(x) = 60,000 + 300x (A) Find the average cost per unit if 500 frames are produced. (B) Find the marginal average cost at a
In Problems 19-42, use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x) = 5 + 3√x
In Problems 32–35, find the indicated quantities for y = f(x) = 2x2 + 5x. Ay and dy for x = 2, and Ax dx = 0.1. =
In Problems 29–38, find each limit if it exists. X lim x→→3 x + 5
In Problems 33–36, (A) Find Ay and dy for the function f at the indicated value of x. (B) Graph Ay and dy from part (A) as functions of Ax. (C) Compare the values of Ay and dy from part (A) at the
In Problems 33–42, use - ∞ or ∞ where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes. h(x) +4 x²2²-4
Find the indicated derivatives in Problems 33–56. dy dt if y = 2 + 5t - 8t³
In Problems 19-42, use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x) = 3-7√x
In Problems 29–38, find each limit if it exists. lim x-4 x-2 X
In Problems 33–36, (A) Find Ay and dy for the function f at the indicated value of x. (B) Graph Ay and dy from part (A) as functions of Ax. (C) Compare the values of Ay and dy from part (A) at the
The total profit (in dollars) from the sale of x skateboards is(A) Find the exact profit from the sale of the 26th skateboard. (B) Use marginal profit to approximate the profit from the sale of the
Find the indicated derivatives in Problems 33–56. y' for y = 5x 2 + 9x¹
In Problems 19-42, use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x) = 10√x + 5
Problems 36–38 refer to the function. S.x² f(x) = (8 - x if x ≥ 2 which is graphed in the figure. f(x) 10- 5 0 5 if 0 ≤ x < 2 Figure for 36-38 10 X
In Problems 29–38, find each limit if it exists. lim V5x + 4 x-1
In Problems 37–40, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If the graph of the function y = f(x) is a line, then the
In Problems 33–42, use - ∞ or ∞ where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes. F(x) 4 x² + 4
In Problems 19-42, use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x) = 16√x +9
Problems 36–38 refer to the function. S.x² f(x) = (8 - x if x ≥ 2 which is graphed in the figure. f(x) 10- 5 0 5 if 0 ≤ x < 2 Figure for 36-38 10 X
In Problems 29–38, find each limit if it exists. lim V16 - 7x x-0
In Problems 37–40, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If the graph of the function y = f(x) is a parabola, then
In Problems 33–42, use - ∞ or ∞ where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes. zł - 6 6 + zł G(x)
Find the indicated derivatives in Problems. d du -(5uº.3 - 4u².2)
In Problems 19-42, use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x) = 1 x - 4
In Problems 37–40, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. Suppose that y= f(x) defines a differentiable function
Find the indicated derivatives in Problems 33–56. d du -(2u4.5 3.1u+ 13.2)
In Problems 19-42, use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x) = 1 x + 4
In Problems 37–40, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. Suppose that y = f(x) defines a function whose domain
Find the indicated derivatives in Problems 33–56. h' (t) if h(t) = 2.1 +0.5t - 2.1 +0.5t 1.17³
In Problems 19-42, use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x) = X x + 1
In Problems 33–42, use - ∞ or ∞ where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes. T(x) = 8x 16 + 16x² x48x³
Find the indicated derivatives in Problems 33–56. F' (t) if F(t) = 0.21³ 3.1t + 13.2 -
In Problems 19-42, use the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). f(x) X x + 2
Find the indicated derivatives in Problems 33–56. y' if y = 2 4 5x+
The price p (in dollars) and the demand x for a brand of running shoes are related by the equation x = 4,000 - 40p(A) Express the price p in terms of the demand x, and find the domain of this
In Problems 43–46, find the indicated derivative and simplify. dy dx for y 1 -X 3 ú 5x2+1
Problems 43 and 44 refer to the graph of y = f(x) = x2 + x shown. -5 f(x) 20 + 15 10 f(x) = x2 + x 5 我
Find the indicated derivatives in Problems 33–56. w' if w= 7 5u²
In Problems 43–46, find the indicated derivative and simplify. y' for y = 3√x 2 + 5 3√x
Problems refer to the graph of y = f(x) = x2 + x shown. -5 f(x) 20 15 10 S f(x) = x² + x 5 ·X
Find the indicated derivatives in Problems 33–56. d (3x² dx 2 7 5x²
In Problems 43–46, find the indicated derivative and simplify. g'(x) for g(x) = 1.8√x + 0.9 X
In Problems 73–76, give a pair of limit expressions that describe the end behavior of the function. f(x) = 45x - x³
In Problems 67–72, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If f is a function such that f(0) exists, then lim
In Problems 43–46, find the indicated derivative and simplify. dy for y dx 6x² + 5 7x4
Find the indicated derivatives in Problems 33–56. NAS + +6 S (n)(n),5
Find the indicated derivatives in Problems 33–56. H' (w) if H(w) 5 w6 - 2Vw
For y = f(x) = x2 + 4, find(A) The slope of the graph at x = 1 (B) The equation of the tangent line at x = 1 in the form y = mx + b.
Find the indicated derivatives in Problems 33–56. d du - (3u²/3 - 5u¹/³)
In Problems, find the value(s) of x where the tangent line is horizontal. f(x) = 10x - x2
In Problems 48 and 49, find the value(s) of x where the tangent line is horizontal. 2 ƒ(x) = ²x³. tr - 3 5x²- 12x + 101
The average pulse rate y (in beats per minute) of a healthy person x inches tall is given approximately by y = 590 Vx 30≤x≤ 75
In Problems 50 and 51, approximate (to four decimal places) the value(s) of x where the graph of f has a horizontal tangent line. f(x) = x4 - 2x3 - 5x2 + 7x
Find the indicated derivatives in Problems 33–56. d -(8u³/4 + 4u-1/4) du
In Problems 51–64, find all horizontal and vertical asymptotes. f(x) = 2x x + 2

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