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mathematics
applied calculus

Questions and Answers of Applied Calculus

Decide which curves are graphs of functions. y X
Factor the polynomials.x3 - 1/8
The function f (r), which gives the cost (in cents) of constructing a 100-cubic-inch cylinder of radius r inches. The graph of f (r) is shown in Fig. 16.For what value(s) of r is the cost 330 cents?
Compute the numbers.1-1.2
The function f (r), which gives the cost (in cents) of constructing a 100-cubic-inch cylinder of radius r inches. The graph of f (r) is shown in Fig. 16.Interpret the fact that the point (3, 162) is
Each quadratic function has the form y = ax2 + bx + c. Identify a, b, and c.y = 3 - 2x + 4x2
Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions.f (x) + h(x)
Letand h(x) = x3 - 5x2 + 1. Calculate the following functions.g(h(t)) 1 − x' (x)8'9x = (x) f
Factor the polynomials.x2 - 14x + 49
Each quadratic function has the form y = ax2 + bx + c. Identify a, b, and c.y = 1 - x2
Decide which curves are graphs of functions. X h
Use the laws of exponents to compute the numbers.51/3 · 2001/3
Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions.g(x) - h(x - 3)
Factor the polynomials.x2 + x + 1/4
The cost function in Fig. 18.If 500 units of goods are produced, estimate the cost of producing 100 more units of goods? Y 3397 2875 500 700 Figure 18 A cost function. y = C(x)
Each quadratic function has the form y = ax2 + bx + c. Identify a, b, and c.y = 1/2x2 + 23x - π
Use the laws of exponents to compute the numbers.(31/3 · 31/6)6
Let f (x) = x2. Graph the functions f (x) + 1, f (x) - 1, f (x) + 2, and f (x) - 2. Make a guess about the relationship between the graph of a general function f (x) and the graph of f (x) + c for
Evaluate each of the functions at the given value of x.f (x) = |x|, x = -2.5
The function f (r), which gives the cost (in cents) of constructing a 100-cubic-inch cylinder of radius r inches. The graph of f (r) is shown in Fig. 16.Interpret the fact that the point (3, 162) is
Letand h(x) = x3 - 5x2 + 1. Calculate the following functions.f (h(x)) 1 − x' (x)8'9x = (x) f
The function f (r), which gives the cost (in cents) of constructing a 100-cubic-inch cylinder of radius r inches. The graph of f (r) is shown in Fig. 16.What is the additional cost of increasing the
Decide which curves are graphs of functions. ທ X
Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions.f (x) + g(x)
Decide which curves are graphs of functions. y X
Find the points of intersection of the pairs of curves.y = 2x2 - 5x - 6, y = 3x + 4
Sketch the graphs of the following functions.Sketch the parabola f (x) = 2x2 - 4x.
Use the laws of exponents to compute the numbers.61/3 · 62/3
Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(√x - 1). Determine the following functions.f (g(x))
If f (x) = x2, find f (x + h) - f (x) and simplify.
Sketch the graphs of the following functions. f(x) = 3 2x + 1 for x < 2 for x ≥ 2
Use the laws of exponents to compute the numbers. 104 54
The function f (r), which gives the cost (in cents) of constructing a 100-cubic-inch cylinder of radius r inches. The graph of f (r) is shown in Fig. 16.How much is saved by increasing the radius
Find the points of intersection of the pairs of curves.y = x2 - 10x + 9, y = x - 9
Decide which curves are graphs of functions. y X
Sketch the graphs of the following functions.Sketch the parabola g(t) = -t2 + 4t - 3.
Use the laws of exponents to compute the numbers.(94/5)5/8
Decide which curves are graphs of functions. y X
Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(√x - 1). Determine the following functions.g(f (x))
If g(t) = 4t - t2, findand simplify. g(t + h) - g(t) h
If f (x) = 1/x, find f (x + h) - f (x) and simplify.
The cost and revenue functions in Fig. 17. The cost of producing x units of goods is C(x) dollars and the revenue from selling x units of goods is R(x) dollars.What are the revenue and cost from the
The cost and revenue functions in Fig. 17. The cost of producing x units of goods is C(x) dollars and the revenue from selling x units of goods is R(x) dollars.At what level of production is the
Sketch the graphs of the following functions. f(x) = Jx 2x3 for 0 for 4 ≤x≤5 < x < 4
Use the laws of exponents to compute the numbers. 35/2 31/2
Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(√x - 1). Determine the following functions.g(h(x))
If g(t) = t3 + 5, findand simplify. g(t + h) = g(t) h
Find the points of intersection of the pairs of curves.y = 3x2 + 9, y = 2x2 - 5x + 3
Relate to the function whose graph is sketched in Fig. 12.Find f (0) and f (7). Y (2, 3) A 1 3 5 Figure 12 (7, -1) 9 y = f(x) X
Sketch the graphs of the following functions. 4- x - 2 2x 2 x + 1 f(x) = 2x for 0 < x < 2 for 2 ≤ x < 3 for x ≥ 3
Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(√x - 1). Determine the following functions.h(g(x))
Sketch the graphs of the following functions. 4x f(x)=8- 4x 84x 2x 4 - for 0 < x < 1 for 1 x < 2 for x ≥ 2
Find the points of intersection of the pairs of curves.y = x3 - 3x2 + x, y = x2 - 3x
The cost and revenue functions in Fig. 17. The cost of producing x units of goods is C(x) dollars and the revenue from selling x units of goods is R(x) dollars.At what level of production is the cost
Relate to the function whose graph is sketched in Fig. 12.Find f (2) and f (-1). Y (2, 3) A 1 3 5 Figure 12 (7, -1) 9 y = f(x) X
Use the laws of exponents to compute the numbers.(21/3 · 32/3)3
Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(√x - 1). Determine the following functions.f (h(x))
Relate to the function whose graph is sketched in Fig. 12.Is f (4) positive or negative? Y (2, 3) A 1 3 5 Figure 12 (7, -1) 9 y = f(x) X
After t hours of operation, an assembly line has assembled A(t) = 20t - 1/2 t2 power lawn mowers, 0 ≤ t ≤ 10. Suppose that the factory’s cost of manufacturing x units is C(x) dollars, where
The cost and revenue functions in Fig. 17. The cost of producing x units of goods is C(x) dollars and the revenue from selling x units of goods is R(x) dollars.What is the profit from the manufacture
Find the points of intersection of the pairs of curves.y = 1/2x3 - 2x2, y = 2x
Table 1 shows a conversion table for men’s hat sizes for three countries. The function g(x) = 8x + 1 converts from British sizes to French sizes, and the function f (x) = 1/8 x converts from French
Use the laws of exponents to compute the numbers.200.5 · 50.5
Use the laws of exponents to compute the numbers. 8 2/3 27
Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(√x - 1). Determine the following functions.h(f (x))
During the first 1/2 hour, the employees of a machine shop prepare the work area for the day’s work. After that, they turn out 10 precision machine parts per hour, so the output after t hours is f
Find the points of intersection of the pairs of curves.y = 1/2x3 + x2 + 5, y = 3x2 - 1/2x + 5
Evaluate each of the functions at the given value of x.f (x) = x100, x = -1
Simplify (81)3/4, 85/3, and (.25)-1.
Exercises relate to the function whose graph is sketched in Fig. 12.Is f (6) positive or negative? Y (2, 3) A 1 3 5 Figure 12 (7, -1) 9 y = f(x) X
The cost function in Fig. 18.The point (1000, 4000) is on the graph of the function. Restate this fact in terms of the function C(x). Y 3397 2875 500 700 Figure 18 A cost function. y = C(x)
The cost function in Fig. 18.Translate the task “solve C(x) = 3500 for x” into a task involving the graph of the function. Y 3397 2875 500 700 Figure 18 A cost function. y = C(x)
The cost function in Fig. 18.Translate the task “find C(400)” into a task involving the graph. Y 3397 2875 500 700 Figure 18 A cost function. y = C(x)
Find the points of intersection of the pairs of curves.y = 30x3 - 3x2, y = 16x3 + 25x2
Solve the equations 21 X - x = 4
Relate to the function whose graph is sketched in Fig. 12.What is the range of f ? Y (2, 3) A 1 3 5 Figure 12 (7, -1) 9 y = f(x) X
Evaluate each of the functions at the given value of x.f (x) = x5, x = 1/2
Use the laws of exponents to compute the numbers.(125 · 27)1/3
Use the laws of exponents to compute the numbers. 74/3 71/3
Simplify (100)3/2 and (.001)1/3.
Let f (x) = x2. Graph the functions f (x + 1), f (x - 1), f (x + 2), and f (x - 2). Make a guess about the relationship between the graph of a general function f (x) and the graph of f (g(x)), where
The revenue R(x) (in thousands of dollars) that a company receives from the sale of x thousand units is given by R(x) = 5x - x2. The sales level x is in turn a function f (d) of the number d of
Solve the equations x + 2 x 6 3
Exercises relate to the function whose graph is sketched in Fig. 12.For what values of x does f (x) = 0? Y (2, 3) A 1 3 5 Figure 12 (7, -1) 9 y = f(x) X
Evaluate each of the functions at the given value of x.f (x) = | x|,x = 10-2
The population of a city is estimated to be 750 + 25t + .1t2 thousand people t years from the present. Ecologists estimate that the average level of carbon monoxide in the air above the city will be
Relate to the function whose graph is sketched in Fig. 12.For what values of x is f (x) ≤ 0? Y (2, 3) A 1 3 5 Figure 12 (7, -1) 9 y = f(x) X
Sketch the graph of f (x) = (x - 1)2 + 2 without using a graphing calculator. Check your result with a graphing calculator.
Sketch the graph of f (x) = (x - 1)2 + 2 without using a graphing calculator. Check your result with a graphing calculator.
The profit function in Fig. 19.The point (2500, 52,500) is the highest point on the graph of the function. What does this say in terms of profit versus quantity? 52,500 y y = P(x) 2500 Figure 19 A
Use the laws of exponents to simplify the algebraic expressions. (√x + 1)4
Solve the equations .x + 14 x+4 = 5
Evaluate each of the functions at the given value of x.f (x) = | x|, x = π
Use the laws of exponents to compute the numbers.(61/2)0
Sketch the graph of f (x) = (x + 2)2 - 1 without using a graphing calculator. Check your result with a graphing calculator.
The profit function in Fig. 19.The point (1500, 42,500) is on the graph of the function. Restate this fact in terms of the function P(x). 52,500 y y = P(x) 2500 Figure 19 A profit function. x
Solve the equations 1 5 6 + 2 X²
The function whose graph is sketched in Fig. 12.For what values of x is f (x) ≥ 0? Y (2, 3) A 1 3 5 Figure 12 (7, -1) 9 y = f(x) X
Compute f (1), f (2), and f (3). 3/(4x) f(x) = 2x √₁²-5 for x < 2 for 2 for 3 ≤ x x < 3
Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents.(xy)6

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