C represents the total cost (in dollars) of producing x units of a product and R represents the total revenue (in dollars) from the sale of x units. How many units must the company sell to break even? (Round your answer to the nearest integer.) C = 2.2x + 10,000, R = 4.9x x = units
The resistance y in ohms of 1000 feet of solid metal wire at 77∘F can be approximated by the model y = 12,000 x2 − 0.38, 5 ≤ x ≤ 100 where x is the diameter of the wire in mils (0.001 in). If the diameter of the wire is doubled, the resistance is changed by approximately what factor? In determining your answer, you can ignore the constant -0.38. 5 4 1/2 1/5 1/4
Find the sales necessary to break even R = C if the cost C of producing x units is C = 5.6 x + 30,000 and the revenue R for selling x units is R = 3.26x. Round your answer to the nearest integer. x ≈ 9,376 units x ≈ 4,767 units x ≈ 9,369 units x ≈ 9,414 units x ≈ 4,774 units
A moving conveyor is built to rise 1 meter for every 7 meters of horizontal change. Suppose the conveyor runs between two floors in a factory. Find the length of the conveyor if the vertical distance between floors is 10 meters. Round your answer to the nearest meter.
The horsepower H required to overcome wind drag on a certain automobile is approximated by H(x) = 0.003x2 + 0.004x − 0.023, 10 ≤ x ≤ 100, where x is the speed of the car in miles per hour. Find H(x/1.1). Round the numerical values in your answer to five decimal places. A) H(x/1.1) = 0.00225x2 + 0.00248x − 0.00364 B) H(x/1.1) = 0.00248x2 + 0.00225x − 0.02300 C) H(x/1.1) = 0.00248x2 + 0.00364x − 0.02300 D) H(x/1.1) = 0.00364x2 + 0.00248x − 0.02300 E) H(x/1.1) = 0.00225x2 + 0.00364x − 0.02300
Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. Find the area of the shaded region. y = f(x) A. calculus, 16 B. precalculus , 11 C. calculus , 11 D. precalculus , 13 E. precalculus , 16
Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. Find the distance traveled in 14 seconds by an object moving with a velocity of v(t) = 12 + 4cost feet per second. A. precalculus, 168.5469 ft B. precalculus , 171.9624 ft C. precalculus , 169.8969 ft D. calculus , 171.9624 ft E. calculus, 168.5469 ft
Use the rectangles in the following graph to approximate the area of the region bounded by y = cosx, y = 0, x = −π/2, and x = π/2.3.1400 1.5700 0.7850 1.1775 2.0933
Use the rectangles in the graph given below to approximate the area of the region bounded by y = 4 x, y = 0, x = 1, and x = 4. Round your answer to three decimal places. 6.37 units2 3.585 units2 2.481 units2 6.872 units2 6.903 units2
Consider the length of the graph of f(x) = 6 x from (1, 6) to (6, 1). Approximate the length of the curve by finding the sum of the lengths of fiveline segments, as shown in following figure. Round your answer to two decimal places. 7.07 8.76 7.76 9.77 9.9
Use the rectangles in the following graph to approximate the area of the region bounded by y = sinx, y = 0, x = 0, and x = π. A. 0.9481 B. 1.2704 C. 1.4221 D. 3.7922 E. 1.8961
Decide whether the following problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution. A cyclist is riding on a path whose elevation is modeled by the function f(x) = 0.14x where x and f(x) are measured in miles. Find the rate of change of elevation when x = 3.5. Round your answer to two decimal places, if necessary. calculus, 0.98 precalculus, 0.14 calculus, 0.14 precalculus, 0.98 precalculus, 0.39
Consider the function f(x) = 10x − x2 and the point P(3, 21) on the graph of f. Find the slope of the secant line passing through P(3, 21) and Q(x, f(x)) for x = 1. Round your answer to one decimal place. 7.5 6.0 4.0 5.5 4.0
Consider the function f(x) = x and the point P(4, 2) on the graph of f. Estimate the slope m of the tangent line of f at P(4, 2). Round your answer to four decimal places, m = 0.2500 m = 0.1663 m = 0.4633 m = 0.1250 m = 0.1667
Let f(x) = { x2 + 2, x ≠ 1 1, x = 1. Determine the following limit. (Hint: Use the graph to calculate the limit. ) limx→1 f(x) A. 2 B. 3 C. 1 D. does not exist. E. 4
Determine the following limit. (Hint: Use the graph to calculate the limit.) limx→1 (6−x) A. 5 B. 1 C. does not exist D. 6 E. 7
Complete the table and use the result to estimate the limit. limx→0 cos(−5x)−1 −5x −1 x = -0.1 -0.01 -0.001 0.001 0.01 0.1 f(x) −0.5 0 0.5 1
Let f(x) = { 3−x, x ≠ 10, x = 1 Determine the following limit. (Hint: Use the graph to calculate the limit. ) limx→1 f(x) a. 4 b. 3 c. 2 d. 0 e. does not exist
Complete the table and use the result to estimate the limit. Use a graphing utility to verify your result. (Round your answers to three decimal places. ) limx→0 1−e2x 4x x -0.1 -0.01 -0.001 0.001 0.01 0.1 f(x) limx→0 1−e2x 4x =
Complete the table and use the result to estimate the limit. Use a graphing utility to verify your result. (Round your answers to four decimal places. ) limx→∞ 7x 7x2 − 5x x 1 10 102 103 104 105 f(x) limx→∞ 7x 7x2 − 5x =
Consider the following function. f(x) = 1 (x−2)2 Determine whether f(x) approaches ∞ or −∞ as x approaches 2 from the left and from the right. (a) limx→2− f(x) (b) limx→2+ f(x)
Consider the following function and graph. f(x) = 1 x+2 Determine whether f(x) approaches ∞ or −∞ as x approaches -2 from the left and from the right. (a) limx→−2− f(x) (b) limx→−2+ f(x)
Determine whether f(x) approaches ∞ or −∞ as x approaches 2 from the left and from the right. f(x) = sec πx 4 limx→2− sec πx 4 = limx→2+ sec πx 4 =
Consider the following function and graph. f(x) = 6|x x2 − 4| Determine whether f(x) approaches ∞ or −∞ as x approaches 2 from the left and from the right. (a) limx→2− f(x) (b) limx→2+ f(x)
Use the information to determine the limits. (If the limit is infinite, enter '∞' or '-∞', as appropriate. If the limit does not otherwise exist, enter DNE.) limx→c f(x) = ∞limx→c g(x) = −2 (a) limx→c [f(x)+g(x)] (b) limx→c [f(x)g(x)] (c) limx→c g(x)f(x)
Consider the following function. f(x) = 1 x2−4 Complete the following table. (Round your answers to two decimal places.) Use the table to determine whether f(x) approaches ∞ or −∞ as x approaches -2 from the left and from the right. limx→−2− f(x) = limx→−2+ f(x) = Use a graphing utility to graph the function to confirm your answer.
Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer if necessary. If an answer does not exist, enter DNE.) f(x) = 9 (x−6)3
Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer if necessary. If an answer does not exist, enter DNE. ) g(t) = t−3 t2+9
Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer if necessary. If an answer does not exist, enter DNE. ) T(t) = 3 − 4 t2
Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer if necessary. If an answer does not exist, enter DNE.) f(z) = ln(z2 − 9) (smaller value) (larger value)
Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer if necessary. If an answer does not exist, enter DNE.) f(x) = 4 tan(πx)
Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary integer if necessary. If an answer does not exist, enter DNE. ) g(x) = 12 x3 − 4x2 + 6x 3x2 − 24x + 36
Determine whether the graph of the function has a vertical asymptote or a removable discontinuity at x = −6. Graph the function using a graphing utility to confirm your answer. f(x) = x2−36 x+6 vertical asymptote removable discontinuity
On a trip of d miles to another city, a truck driver's average speed was x miles per hour. On the return trip the average speed was y miles per hour. The average speed for the round trip was 60 miles per hour. (a) Verify the following. y = 30x x−30 What is the domain? x < 30 x > 30 x ≠ 30 x > 0 R (b) Complete the table. (Round your answers to three decimal places. ) (c) Find the limit of y as x → 30+. (If the limit does not exist, enter DNE.)