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college mathematics for business

Questions and Answers of College Mathematics For Business

If f(5) = 4, f′(5) = -1, g(5) = 2, and g′(5) = -3, then find h′(5) for each of the following functions:(A) h(x) = 3f(x)(B) h(x) = -2g(x)(C) h(x) = 2f(x) + 5(D) h(x) = -g(x) - 1(E) h(x) = 2f(x)
In Problem find the indicated function if cost and revenue are given by C(x) = 145 + 1.1x and R(x) = 5x - 0.02x2, respectively.Marginal profit function
In Problem find f′(x) and simplify. 5x3 3 f(x) 2x 4 +
In Problem find f′(x) and simplify. f(x) = 0.5 + 0.25x
In Problem evaluate dy and Δy for each function for the indicated values.y = f (x) = x2 - 3x + 2; x = 5, dx = Δx = 0.2
In Problem find the indicated function if cost and revenue are given by C(x) = 145 + 1.1x and R(x) = 5x - 0.02x2, respectively.Average profit function
In Problem find the indicated function if cost and revenue are given by C(x) = 145 + 1.1x and R(x) = 5x - 0.02x2, respectively.Marginal average profit function
In Problem find f′(x) and simplify.f(x) = 5
Problem refer to the function.which is graphed in the figure.Solve each inequality. Express answers in interval notation.(A) f(x) < 0 (B) f(x) ≥ 0 Sx² 8 - x if 0
In Problem find f′(x) and simplify.f(x) = (3x3 - 2) (x + 1)
Problem refer to the function.which is graphed in the figure. Sx² 8 - x if 0
In Problem find the indicated quantities for y = f(x) = x2 + x.Δx, Δy, and Δy/Δx for x1 = 1 and x2 = 3
The total cost (in dollars) of producing x food processors isC(x) = 2,000 + 50x - 0.5x2(A) Find the exact cost of producing the 21st food processor.(B) Use marginal cost to approximate the cost of
In Problem find the indicated quantities for y = f(x) = x2 + x.[f(x1 + Δx) - f(x1)] / Δx for x1 = 1 and Δx = 2.
In Problem find the indicated quantities for y = f(x) = x2 + x.dy for x1 = 1 and x2 = 3.
In Problem find the indicated quantities for y = f(x) = x2 + x.Δy and dy for x = 1, Δx = dx = 0.2.
The total profit (in dollars) from the sale of x skateboards isP(x) = 30x - 0.3x2 - 250 0 ≤ x ≤ 100(A) Find the exact profit from the sale of the 26th skateboard.(B) Use marginal profit to
For a company that manufactures tennis rackets, the average cost per racket C ̅ iswhere x is the number of rackets produced per hour. What will the approximate change in average cost per
The total profit (in dollars) from the sale of x sweatshirts isP(x) = 5x - 0.005x2 - 450 0 ≤ x ≤ 1,000Evaluate the marginal profit at the given values of x, and interpret the results.(A) x =
Let f(x) = 0.5x2 - 5.(A) Find the slope of the secant line through (2, f(2)) and (4, f(4)).(B) Find the slope of the secant line through (2, f(2)) and (2 + h, f(2 + h)), h ≠ 0.(C) Find the slope of
A particular person learning to type has an achievement record given approximately bywhere N is the number of words per minute typed after t weeks of practice. What is the approximate improvement
Find dy and Δy for y = 52√x, x = 4, and Δx = dx = 0.3.
A company will sell N units of a product after spending $x thousand in advertising, as given byN = 60x - x2 5 ≤ x ≤ 30Approximately what increase in sales will result by
In Problem determine where f is continuous. Express the answer in interval notation. f(x) = V4 – x²
In Problem evaluate the indicated limits if they exist. x + 1 Let f(x) Find (3 – x)2" %3D (A) lim f(x) (B) lim f(x) (C) lim f(x)
In Problem find the value(s) of x where the tangent line is horizontal.f(x) = x3 + 3x2 - 45x - 135
In Problem determine where f is continuous. Express the answer in interval notation. х + 4 f(x) х + 3х — 4
A drug is given to a patient to dilate her arteries. If the radius of an artery is increased from 2 to 2.1 millimeters, approximately how much is the cross-sectional area increased? [Assume that the
In Problem determine where f is continuous. Express the answer in interval notation. x + 1 f(x) x - 2
In Problem determine where f is continuous. Express the answer in interval notation. f(x) = V4 – x² 2
In Problem evaluate the indicated limits if they exist. |x - 4| Find Let f(x) x - 4 (A) lim f(x) (B) lim f(x) r4+ (C) lim f(x)
The price–demand equation and the cost function for the production of garden hoses are given, respectively, by p = 20 - √x and C(x) = 500 + 2xwhere x is the number of garden hoses that can
In Problem evaluate the indicated limits if they exist. 2x Let f(x) Find x? - 3x (A) lim f(x) (B) lim f(x) (C) lim f(x)
If an object moves along the y axis (scale in feet) so that it is at y = f(x) = 8x2 - 4x + 1 at time x (in seconds), find(A) The instantaneous velocity function(B) The velocity at time x = 3 seconds
An object moves along the y axis (scale in feet) so that at time x (in seconds) it is at y = f(x) = -5x2 + 16x + 3. Find(A) The instantaneous velocity function(B) The time(s) when the velocity is 0
Let f(x) = x3, g(x) = (x - 4)3, and h(x) = x3 - 4.(A) How are the graphs of f, g, and h related? Illustrate your conclusion by graphing f, g, and h on the same coordinate axes.(B) How would you
In Problem evaluate the indicated limits if they exist. x - 3 Let f(x) Find 9 - x2 (A) lim f(x) (B) lim f(x) (C) lim f(x) X-3
In Problem evaluate the indicated limits if they exist. x2 - x - 2 Let f(x) Find 7x + 10 %3D (A) lim f(x) (B) lim f(x) (C) lim f(x)
In Problem determine where f is continuous. Express the answer in interval notation.f(x) = x2 - 4
In Problem evaluate the indicated limits if they exist. 2r Let f(x) Find 3(х — 2)2 (A) lim f(x) (B) lim f(x) (C) lim f(x)
In Problem evaluate the indicated limits if they exist. 2x Let f(x) Find 3(x – 2)3" (A) lim f(x) (B) lim f(x) (C) lim f(x)
In Problem evaluate the indicated limits if they exist. f(x + h) - f(xr) lim h0 1 for f(x) h x + 2
In Problem evaluate the indicated limits if they exist. f(2 + h) - f(2) lim for f(x) = x2 + 4
Problem refer to the function f in the figure. Determine whether f is differentiable at the indicated value of x.x = -1 f(x) 4 -2 5
Problem refer to the function f in the figure. Determine whether f is differentiable at the indicated value of x.x = 0 f(x) 4 -2 5
Problem refer to the function f in the figure. Determine whether f is differentiable at the indicated value of x.x = 1 f(x) 4 -2 5
Problem refer to the function f in the figure. Determine whether f is differentiable at the indicated value of x.x = 3 f(x) 4 -2 5
Problem refer to the function f in the figure. Determine whether f is differentiable at the indicated value of x.x = 4 f(x) 4 -2 5
In Problem find all horizontal and vertical asymptotes. -2x + 5 f(x) (x - 4)2
In Problem find all horizontal and vertical asymptotes. 5x f(x) x - 7
In Problem use the definition of the derivative and the four-step process to find f′(x).f(x) = x2 - x
In Problem use the definition of the derivative and the four-step process to find f′(x).f(x) = √x - 3
In Problem find all horizontal and vertical asymptotes. x? + 9 f(x) x - 3 ||
In Problem find all horizontal and vertical asymptotes. x? – 9 f(x) x* + x - 2
The domain of the power function f(x) = x1/3 is the set of all real numbers. Find the domain of the derivative f = (x).Discuss the nature of the graph of y = f(x) for any x values excluded from the
The total cost (in dollars) of producing x HDTVs isC(x) = 10,000 + 200x - 0.1x2(A) Find the exact cost of producing the 101st TV.(B) Use the marginal cost to approximate the cost of producing the
The total cost (in dollars) of producing x bicycles isC(x) = 5,000 + 40x + 0.05x2(A) Find the total cost and the marginal cost at a production level of 100 bicycles and interpret the results.(B) Find
The total cost (in dollars) of producing x laser printers per week is shown in the figure. Which is greater, the approximate cost of producing the 201st printer or the approximate cost of producing
A company producing computer components has established that, on average, a new employee can assemble N(t) components per day after t days of on-the-job training, as given by(A) Find the average rate
Letp = 25 - 0.01x and C(x) = 2x + 9,000 0 ≤ x ≤ 2,500be
Table 3 contains price–demand and total cost data from a bakery for the production of kringles (a Danish pastry), where p is the price (in dollars) of a kringle for a daily demand of x kringles and
The total number of swimming pools, N (in thousands), sold during a year is given bywhere t is the number of months since the beginning of the year. Find N(9) and N′(9), and interpret these
A sewage treatment plant uses a pipeline that extends 1 mile toward the center of a large lake. The concentration of sewage C(x) in parts per million, x meters from the end of the pipe is given
The body temperature (in degrees Fahrenheit) of a patient t hours after taking a fever-reducing drug is given byF(t) = 0.16 t2 - 1.6 t + 102Find F(4) and F′(4). Write a brief verbal interpretation
If a person learns N items in t hours, as given byN(t) = 20√tfind the rate of learning after(A) 1 hour (B) 4 hours
The coefficient of thermal expansion (CTE) is a measure of the expansion of an object subjected to extreme temperatures. We want to use a Michaelis–Menten function of the formwhere C = CTE, T is
In Problem sketch a possible graph of a function that satisfies the given conditions. f(-2) = 2; lim f(x) 1; lim f(x) = 1 %3| X-2*
Problem refer to the function F in the graph shown. Use the graph to determine whether F'(x) exists at each indicated value of x.x = a F(x) a b c d e f 8 h
In Problem find all horizontal and vertical asymptotes. 2x2 + 7x + 12 f(x) %3D 2x2 + 5x – 12
If an object moves along the y axis (marked in feet) so that its position at time x (in seconds) is given by the indicated functions in Problem find(A) The instantaneous velocity function v =
In Problem find all horizontal and vertical asymptotes. 2r2 f(x) = 2x - 5x + 2 x? - x - 2
In Problem find each indicated quantity if it exists. (x + 2)2 Find Let f(x) 2 - 4 (A) lim f(x) (B) lim f(x) X-2 (C) lim f(x)
In Problem determine whether f is differentiable at x = 0 by consideringf(x) = √1- x2 f(0 + h) - f(0) lim h0 h
If an object moves along the y axis (marked in feet) so that its position at time x (in seconds) is given by the indicated functions in Problem find(A) The instantaneous velocity function v =
Compute the following limit for each function in Problemf(x) = | x + 1| f(2 + h) - f(2) lim h0 h
In Problem write the expression in the form xn.√x
Problem refer to the following graph of y = f(x). 3+ 2+ -2 2 -1+ -2 -3+
In Problem write the expression in the form xn.(x4)3
In Problem find (A) The leading term of the polynomial, (B) The limit as x approaches ∞ (C) The limit as x approaches - ∞.P(x) = x4 + 2x5 - 11x
Problem refer to functions f and g that satisfy f'(2) = 3 and g′(2) = -1. In each problem, find h′(2) for the indicated function h.h(x) = 2f(x) - 3g(x) + 7
In Problem use the four-step process to find f'(x) and then find f' (1), f' (2), and f' (3). f(x) = 10VX + 5
In Problem use the four-step process to find f'(x) and then find f' (1), f' (2), and f' (3). 1 f(x) %3D х — 4
In Problem find all partition numbers of the function. x + x f(x) x? - x - 42
In Problem use - ∞ or ∞ where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes. х2 — 4х — 21 f(x) x — Зх —10 ||
Given that find the indicated limits in Problem lim f(x) = -5 and lim g(x) = 4, %3D
In Problem use - ∞ or ∞ where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes. x? – 1 f(x) x' + 3x + 2x
In Problem use - ∞ or ∞ where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes. x - 4 f(x) + x? – 2x 3
In Problem sketch a possible graph of a function that satisfies the given conditions. f(0) = 1; lim f(x) : 3; lim f(x) = 1 %3D
In Problem use a sign chart to solve each inequality. Express answers in inequality and interval notation.x2 - x - 12 < 0
In Problem use - ∞ or ∞ where appropriate to describe the behavior at each zero of the denominator and identify all vertical asymptotes. х2 + 2х -15 x? + 2х - 8 f(x) %3D
Problem refer to the function F in the graph shown. Use the graph to determine whether F'(x) exists at each indicated value of x.x = b F(x) a b c d e f 8 h
In Problem find each indicated quantity if it exists. (1 - x? ifx s 0 Let f(x) Find l1 +x? ifx > 0' (B) lim f(x) (A) lim f(x) (C) lim f(x) (D) f(0)
In Problem use a sign chart to solve each inequality. Express answers in inequality and interval notation.x2 + 21 > 10x
In Problem find all horizontal and vertical asymptotes. 2x f(x) x + 2
Problem refer to the function F in the graph shown. Use the graph to determine whether F'(x) exists at each indicated value of x.x = c F(x) a b c d e f 8 h
Problem refer to the function F in the graph shown. Use the graph to determine whether F'(x) exists at each indicated value of x.x = d F(x) a b c d e f 8 h
In Problem find all horizontal and vertical asymptotes. x² + 1 f(x) 2 - 1
In Problem find each indicated quantity if it exists. (x? ifx < 1 Find 2x if x > 1 Let f(x) (A) lim f(x) (B) lim f(x) (C) lim f(x) (D) f(1)
In Problem use a sign chart to solve each inequality. Express answers in inequality and interval notation.x3 < 4x
Problem refer to the function F in the graph shown. Use the graph to determine whether F'(x) exists at each indicated value of x.x = e F(x) a b c d e f 8 h

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