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mathematics
college mathematics for business economics

Questions and Answers of College Mathematics For Business Economics

In Problems 47–56, find the indicated derivatives and simplify. f'(x) for f(x) = 3x² 2 2x - 1
In Problems 45–60, find the indicated derivative and simplify. dx EX (x + 1) [ P
In Problems 47–56, find the indicated derivatives and simplify. d dw w²3w+1 w²1 -
In Problems 47–56, find the indicated derivatives and simplify. dy dw for y= w4 - w³. 3w1
In Problems 55–62, use the price–demand equation to find the values of p for which demand is elastic and the values for which demand is inelastic. Assume that price and demand are both
In Problems 45–60, find the indicated derivative and simplify. F' (t) if F(t) = (e²+1)³
In Problems 47–56, find the indicated derivatives and simplify. y' for y = (1 + x - x²) et
In Problems 45–60, find the indicated derivative and simplify. 2 G' (t) if G(t) = (1 - e²¹) ²
In Problems 47–56, find the indicated derivatives and simplify. dy dt for y= (1 + e¹) In t
In Problems 45–60, find the indicated derivative and simplify. y' if y = ln (x² + 3) ³/2
In Problems 55–62, use the price–demand equation to find the values of p for which demand is elastic and the values for which demand is inelastic. Assume that price and demand are both
In Problems 55–62, use the price–demand equation to find the values of p for which demand is elastic and the values for which demand is inelastic. Assume that price and demand are both positive.
In Problems 45–60, find the indicated derivative and simplify. y' if y= [In(x² + 3)]³/2
In Problems 55–62, use the price–demand equation to find the values of p for which demand is elastic and the values for which demand is inelastic. Assume that price and demand are both
In Problems 45–60, find the indicated derivative and simplify. d 1 dw (w³+4)5
In Problems 45–60, find the indicated derivative and simplify. d 1 dw (w²-2)6
In Problems 61-66, find f'(x) and find the equation of the line tangent to the graph of f at x = 2. f(x) = (1 + 3x) (5 - 2x)
In Problems 55–62, use the price–demand equation to find the values of p for which demand is elastic and the values for which demand is inelastic. Assume that price and demand are both positive.
In Problems 63–68, use the demand equation to find the revenue function. Sketch the graph of the revenue function, and indicate the regions of inelastic and elastic demand on the graph. x = f(p)
In Problems 61-66, find f'(x) and find the equation of the line tangent to the graph of f at x = 2. f(x) || 2x - 5 2x - 3
In Problems 63–68, use the demand equation to find the revenue function. Sketch the graph of the revenue function, and indicate the regions of inelastic and elastic demand on the graph. x = f(p)
In Problems 63–68, use the demand equation to find the revenue function. Sketch the graph of the revenue function, and indicate the regions of inelastic and elastic demand on the graph. = f(p)
In Problems 71-74, find f'(x) in two ways: (1) using the product or quotient rule and (2) simplifying first. f(x) = x 1² + 9
In Problems 71-74, find f'(x) in two ways: (1) using the product or quotient rule and (2) simplifying first. f(x) = x³ (x² - 1)
In Problems 71-74, find f'(x) in two ways: (1) using the product or quotient rule and (2) simplifying first. f(x) = x²(x³ - 1)
Domain: All real x, except x = -1; 0 on (-,-1); f"(x) < 0 on"> f(-3) = 2, f(-2) = 3, f(0) = -1, f(1) = 0; f'(x) > 0 on (-∞,-1) and (-1,0); f" (x) > 0 on (-∞, -1); ƒ" (x) < 0 on (-1,0);
Domain: All real x, except x = 1; f(0) = -2, f(2) = 0; f'(x) 0 on (1, ∞ ); 00 vertical asymptote: x = 1; horizontal asymptote: y = -1
Find the indicated derivatives in Problems 9–26. d X-³ dx 18
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
The price p (in dollars) and the demand x for a particular steam iron are related by the equation Where x is the number of saws that can be sold at a price of $p per saw and C(x) is the total cost
In Problems 60–69, evaluate the indicated limits if they exist. Let f(x) = |x4| x - 4 (A) lim f(x) x-4 . Find (B) lim f(x) x-4¹ (C) lim f(x) x-4
In Problems 61–66, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If a function f is continuous on the interval (a, b), then f
In Problems 77–82, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.A rational function is continuous for all but finitely many
Find the indicated derivatives in Problems 77–82. y' if y(2x - 5)²
In Problems 78–82, find all horizontal and vertical asymptotes. f(x) = -2x + 5 (x-4)²
A personal-computer salesperson receives a base salary of $1,000 per month and a commission of 5% of all sales over $10,000 during the month. If the monthly sales are $20,000 or more, then the
In Problems 5–8, find the indicated derivative. y' for y= ln (2x + 7)
In Problems 5-8, find functions E(u) and I(x) so that y = E[I(x)]. 4 p + a = ^
In Problems 5–8, find the indicated derivative. f'(x) for f(x) = In (3 + e)
In Problems 5-8, find functions E(u) and I(x) so that y = E[I(x)]. y = e2x + 3et - 10
In Problems 9-14, assume that x = x(t) and y = y(t). Find the indicated rate, given the other information. y = x² + 2; dx/dt = 3 when x = 5; find dy/dt
In Problems 9-34, find f'(x) and simplify. f(x) = 2x3 (x2 - 2)
In Problems 9-12, find y' in two ways:3x + 5y + 9 = 0(A) Differentiate the given equation implicitly and then solve for y′. (B) Solve the given equation for y and then differentiate directly.
Use a calculator to evaluate A to the nearest cent in Problems 9 and 10. A = $1,000e0.¹ for t = 2, 5, and 8
In Problems 9-34, find f'(x) and simplify. f(x) = 2x + 3 x-2
A point is moving on the graph of xy = 36. When the point is at (4, 9), its x coordinate is increasing by 4 units per second. How fast is the y coordinate changing at that moment?
Find the indicated derivatives in Problems 14–19. d dx (x6 In x)
In Problems 13-30, use implicit differentiation to find y' and evaluate y' at the indicated point.x2 - y3 - 3 = 0; (2, 1)
In Problems 9-34, find f'(x) and simplify. f(x) 3x - 4 2x + 3
In Problems 13-30, use implicit differentiation to find y' and evaluate y' at the indicated point. ² + x³+ 4 = 0; (-2, 2)
Find the indicated derivatives in Problems 14–19. det dx x6
In Problems 9-34, find f'(x) and simplify.f(x) = 3xex
In Problems 13–18, solve for t or r to two decimal places.2 = e5r
In Problems 13-30, use implicit differentiation to find y' and evaluate y' at the indicated point. y² + 2y + 3x = 0; (-1, 1)
Find the indicated derivatives in Problems 14–19. y' for y = ln (2x6 + et)
In Problems 13-30, use implicit differentiation to find y' and evaluate y' at the indicated point. y²-y 4x = 0; (0, 1)
In Problems 9-34, find f'(x) and simplify.f(x) = x2 ex
Find the indicated derivatives in Problems 14–19. f'(x) for f(x) = e³-²
In Problems 13-30, use implicit differentiation to find y' and evaluate y' at the indicated point. ху - 6 = 0; (2, 3)
Find the indicated derivatives in Problems 14–19. dy/dx for y = e2x In 5.x
Find the equation of the line tangent to the graph of y = f(x) = 1 + e* at x = 0. At x = -1.
In Problems 17-38, find f'(x) and simplify. f(x) = (60.5x)4
In Problems 9-34, find f'(x) and simplify.f(x) = (x2 + 1) (2x - 3)
In Problems 17-38, find f'(x) and simplify.f(x) = (3x2 + 5)5
In Problems 13-30, use implicit differentiation to find y' and evaluate y' at the indicated point. 2xy +y + 2 = 0; (-1,2)
In Problems 13-30, use implicit differentiation to find y' and evaluate y' at the indicated point. 2y + xy 1 = 0; (-1, 1)
In Problems 15-24, find the relative rate of change of f(x) at the indicated value of x. Round to three decimal places.f(x) = 9x - 5 ln x; x = 3
In Problems 17-38, find f'(x) and simplify.f(x) = 5ex
In Problems 13-30, use implicit differentiation to find y' and evaluate y' at the indicated point. x²y3x² - 4 = 0; (2,4)
In Problems 9-34, find f'(x) and simplify.f(x) = (0.4x + 2) (0.5x - 5)
In Problems 17-38, find f'(x) and simplify.f(x) = 10 - 4ex
In Problems 15-24, find the relative rate of change of f(x) at the indicated value of x. Round to three decimal places.f(x) = 9x - 5 ln x; x = 7
In Problems 9-34, find f'(x) and simplify. f(x) = ²+1 2x - 3
In Problems 17-38, find f'(x) and simplify.f(x) = e5x
In Problems 13-30, use implicit differentiation to find y' and evaluate y' at the indicated point. e¹= x² + y²; (1,0)
In Problems 25–27, find the logarithmic derivatives. A (t) 400e0.049t
In Problems 25–32, find the percentage rate of change of f(x) at the indicated value of x. Round to the nearest tenth of a percent.f(x) = 75 + 110x; x = 4
In Problems 17-38, find f'(x) and simplify.f(x) = 6e-2x
In Problems 13-30, use implicit differentiation to find y' and evaluate y' at the indicated point. x³y = lny; (1, 1)
In Problems 17-38, find f'(x) and simplify.f(x) = 3e-6x
In Problems 17-38, find f'(x) and simplify. f(x) = et² + 3x+1
A point is moving on the graph of 3y2 + 40x2 = 16 so that its y coordinate is increasing by 2 units per second when (x, y) = (2, 2). Find the rate of change of the x coordinate.
In Problems 13-30, use implicit differentiation to find y' and evaluate y' at the indicated point. In y = 2y² – x; (2, 1)
In Problems 39–46, find the logarithmic derivative. A(t) = 900e0.24t
In Problems 17-38, find f'(x) and simplify. (xu[ + 1) = (x)ƒ
In Problems 17-38, find f'(x) and simplify. f(x) = 2 ln(x²-3x + 4)
In Problems 13-30, use implicit differentiation to find y' and evaluate y' at the indicated point. xe — y = x – 2; (2, 0)
In Problems 13-30, use implicit differentiation to find y' and evaluate y' at the indicated point. x ln y + 2y = 2x³; (1, 1)
In Problems 17-38, find f'(x) and simplify.f(x) = (2x - 5)1/2
Water is leaking onto a floor. The resulting circular pool has an area that is increasing at a rate of 30 square inches per minute. How fast is the circumference C of the pool increasing when the
In Problems 17-38, find f'(x) and simplify. f(x) = (x4 + 1)-²
In Problems 25–32, find the percentage rate of change of f(x) at the indicated value of x. Round to the nearest tenth of a percent.f(x) = 5,100 - 3x2 ; x = 41
In Problems 9-34, find f'(x) and simplify. f(x) ²+1
In Problems 9-34, find f'(x) and simplify. f(x) = 1 et 1 + et
In Problems 25–32, find the percentage rate of change of f(x) at the indicated value of x. Round to the nearest tenth of a percent.f(x) = 3,000 - 8x2 ; x = 18
In Problems 9-34, find f'(x) and simplify. f(x) = In x 1 + x
Find the indicated derivatives in Problems 34–36. y' for y = 72²+4
In Problems 17-38, find f'(x) and simplify.f(x) = 4 - 2 ln x
In Problems 9-34, find f'(x) and simplify. f(x) 2x 1 + ln x
In Problems 17-38, find f'(x) and simplify.f(x) = 8 ln x

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