Determine the integrals by making appropriate substitutions. ∫ e√x /√x dx
> A growth company is one whose net earnings tend to increase each year. Suppose that the net earnings of a company at time t are being generated at the rate of 30 + 5t million dollars per year. (a) Write a definite integral that gives the present value of
> A continuous stream of income is produced at the rate of 20 e1-0.09 t thousand dollars per year at time t, and invested money earns 6% interest. (a) Write a definite integral that gives the present value of this stream of income over the time from t = 2
> Find the present value of a continuous stream of income over 3 years if the rate of income is 80 e-0.08t thousand dollars per year at time t and the interest rate is 11%.
> Divide the given interval into n subintervals and list the value of Δx and the endpoints a0, a1, …. , an of the subintervals. -1 ≤ x ≤ 2; n = 5
> Divide the given interval into n subintervals and list the value of Δx and the endpoints a0, a1, …. , an of the subintervals. 3 ≤ x ≤ 5; n = 5
> Determine the integrals by making appropriate substitutions. ∫ x/√(x2 + 1) dx
> Consider the definite integral ∫0 1 4/ (1 + x2) dx, which has the value π. Suppose the trapezoidal rule with n = 15 is used to estimate π. Graph the second derivative of the function in the window [0, 1] by [-10, 10], and then use the graph to obtain a
> Consider the definite integral ∫0 1 4/ (1 + x2) dx, which has the value π. Suppose the midpoint rule with n = 20 is used to estimate π. Graph the second derivative of the function in the window [0, 1] by [-10, 10], and then use the graph to obtain a bo
> Approximate the integrals by the midpoint rule, the trapezoidal rule, and Simpson’s rule with n = 10. Then, find the exact value by integration and give the error for each approximation. Express your answers to the full accuracy given by the calculator o
> Approximate the integrals by the midpoint rule, the trapezoidal rule, and Simpson’s rule with n = 10. Then, find the exact value by integration and give the error for each approximation. Express your answers to the full accuracy given by the calculator o
> Approximate the integrals by the midpoint rule, the trapezoidal rule, and Simpson’s rule with n = 10. Then, find the exact value by integration and give the error for each approximation. Express your answers to the full accuracy given by the calculator o
> Approximate the integrals by the midpoint rule, the trapezoidal rule, and Simpson’s rule with n = 10. Then, find the exact value by integration and give the error for each approximation. Express your answers to the full accuracy given by the calculator o
> In Fig. 17 a definite integral of the form ∫a b f (x)dx is approximated by the trapezoidal rule. Determine f (x), a, b, and n. Figure 17: NORMAL FLOAT AUTO REAL RADIAN CL (sin(22)+sum (sea(2sin(X²), X.2.5.5.5..5))+sin(62)).25 Ans
> In Fig. 16 a definite integral of the form ∫a b f (x)dx is approximated by the midpoint rule. Determine f (x), a, b, and n. Figure 16: NORMAL FLOAT AUTO REAL RADIAN CL sum(sea(1/(25-X2), X.3.1.4. 4489645238 4489645238 9..2))*.2 An
> Subdivide the interval 0 ≤ t ≤ 22 into n subintervals of length Δt = 22/n seconds. Let ti be a point in the ith subinterval. (a) Show that (R/60)Δt ≈ [number of liters of blood flowing past the monitoring point during the ith time interval]. (b) Show tha
> (a) Suppose that the graph of f (x) is above the x-axis and concave down on the interval a0 ≤ x ≤ a1. Let x1 be the midpoint of this interval, let Δx = a1 - a0, and construct the line tangent to the gra
> Determine the integrals by making appropriate substitutions. ∫ x4/(x5 + 1) dx
> Approximate the value of ∫a b f (x)dx, where f (x) ≥ 0, by dividing the interval a ≤ x ≤ b into four subintervals and constructing five rectangles. (See Fig. 14.) Note that the w
> (a) Show that the area of the trapezoid in Fig. 13(a) is ½ (h + k) l. (b) Show that the area of the first trapezoid on the left in Fig. 13(b) is ½ [ f (a0) + f (a1)]Δx. (c) Derive the trapezoidal rule for the case
> Consider ∫1 2 f (x)dx, where f (x) = 3 ln x. (a) Make a rough sketch of the graph of the fourth derivative of f (x) for 1 ≤ x ≤ 2. (b) Find a number A such that | f ’’ ’’ (x) | ≤ A for all x satisfying 1 ≤ x ≤ 2. (c) Obtain a bound on the error of using
> Consider ∫0 2 f (x)dx, where f (x) = 1/12 x4 + 3x2. (a) Make a rough sketch of the graph of f ’’(x) for 0 ≤ x ≤ 2. (b) Find a number A such that | f ’’(x) | ≤ A for all x satisfying 0 ≤ x ≤ 2. (c) Obtain a bound on the error of using the midpoint rule wi
> In a drive along a country road, the speedometer readings are recorded each minute during a 5-minute interval. Use the trapezoidal rule to estimate the distance traveled during the 5 minutes. Time (minutes) Velocity (mph) 0 1 2 33 32 28 3 30 4 5 32
> Upon takeoff, the velocity readings of a rocket noted every second for 10 seconds were 0, 30, 75, 115, 155, 200, 250, 300, 360, 420, and 490 feet per second. Use the trapezoidal rule to estimate the distance the rocket traveled during the first 10 second
> To determine the amount of water flowing down a certain 100-yard-wide river, engineers need to know the area of a vertical cross section of the river. Measurements of the depth of the river were made every 20 yards from one bank to the other. The reading
> In a survey of a piece of oceanfront property, measurements of the distance to the water were made every 50 feet along a 200-foot side. (See Fig. 12.) Use the trapezoidal rule to estimate the area of the property. Figure 12: 200' 100' 90' 125' 150'
> The following integrals cannot be evaluated in terms of elementary antiderivatives. Find an approximate value by Simpson’s rule. Express your answers to five decimal places. ∫-1 2 √(1 + x4) dx; n = 4
> The following integrals cannot be evaluated in terms of elementary antiderivatives. Find an approximate value by Simpson’s rule. Express your answers to five decimal places. ∫0 2 √(sin x) dx; n = 5
> Determine the integrals by making appropriate substitutions. ∫ √(ln x)/x dx
> The following integrals cannot be evaluated in terms of elementary antiderivatives. Find an approximate value by Simpson’s rule. Express your answers to five decimal places. ∫0 1 1 / (x3 + 1) dx; n = 2
> The following integrals cannot be evaluated in terms of elementary antiderivatives. Find an approximate value by Simpson’s rule. Express your answers to five decimal places. ∫0 2 √(1 + x3) dx; n = 4
> Approximate the following integrals by the midpoint rule, the trapezoidal rule, and Simpson’s rule. Then, find the exact value by integration. Express your answers to five decimal places. ∫1 5 (4x3 - 3x2) dx; n = 2
> Approximate the following integrals by the midpoint rule, the trapezoidal rule, and Simpson’s rule. Then, find the exact value by integration. Express your answers to five decimal places. ∫2 5 x ex dx; n = 5
> Approximate the following integrals by the midpoint rule, the trapezoidal rule, and Simpson’s rule. Then, find the exact value by integration. Express your answers to five decimal places. ∫0 3 x √(4 – x) dx; n = 5
> Approximate the following integrals by the midpoint rule, the trapezoidal rule, and Simpson’s rule. Then, find the exact value by integration. Express your answers to five decimal places. ∫0 2 2x ex2 dx; n = 4 18.
> Approximate the following integrals by the midpoint rule, the trapezoidal rule, and Simpson’s rule. Then, find the exact value by integration. Express your answers to five decimal places. ∫10 20 ln x / x dx; n = 5
> Approximate the following integrals by the midpoint rule, the trapezoidal rule, and Simpson’s rule. Then, find the exact value by integration. Express your answers to five decimal places. ∫1 4 (2x - 3)3 dx; n = 3
> Approximate the following integrals by the trapezoidal rule; then, find the exact value by integration. Express your answers to five decimal places. ∫- 1 e2x dx; n = 2, 4
> Approximate the following integrals by the trapezoidal rule; then, find the exact value by integration. Express your answers to five decimal places. ∫1 5 1/x2 dx; n = 3
> Determine the integrals by making appropriate substitutions. ∫ ln(2x)/x dx
> Approximate the following integrals by the trapezoidal rule; then, find the exact value by integration. Express your answers to five decimal places. ∫4 9 1 / (x – 3) dx; n = 5
> Approximate the following integrals by the trapezoidal rule; then, find the exact value by integration. Express your answers to five decimal places. ∫0 1 (x – ½)2 dx; n = 4
> Approximate the following integrals by the midpoint rule; then, find the exact value by integration. Express your answers to five decimal places. ∫1 2 1/(x + 1) dx; n = 5
> Approximate the following integrals by the midpoint rule; then, find the exact value by integration. Express your answers to five decimal places. ∫0 1 e-x dx; n = 5
> Approximate the following integrals by the midpoint rule; then, find the exact value by integration. Express your answers to five decimal places. ∫1 5 (x - 1)2 dx; n = 2, 4
> Approximate the following integrals by the midpoint rule; then, find the exact value by integration. Express your answers to five decimal places. ∫0 4 (x2 + 5) dx; n = 2, 4
> Refer to the graph in Fig. 11. Apply the trapezoidal rule with n = 4 to estimate the area under the curve. Figure 11: 50 40 30 20 10 01 2 3 4 5 6 7 8 x
> Refer to the graph in Fig. 11. Draw the rectangles that approximate the area under the curve from 0 to 8 when using the midpoint rule with n = 4. Figure 11: 50 40 30 20 10 01 2 3 4 5 6 7 8 x
> Divide the interval into n subintervals and list the value of x and the midpoints x1, .… , xn of the subintervals. -1 ≤ x ≤ 1; n = 4 0 ≤ x ≤ 3; n = 6
> Divide the interval into n subintervals and list the value of x and the midpoints x1, .… , xn of the subintervals. -1 ≤ x ≤ 1; n = 4
> Evaluate the following definite integrals. ∫0 24x (1 + x2)3 dx
> Evaluate the following definite integrals. ∫2 6 1/ √(4x + 1) dx
> Evaluate the following definite integrals. ∫5/2 3 2(2x - 5)14 dx
> Find the are of the shaded region. y=x√√√4x² -2 y 2 X
> Find the area of the shaded regions. -3 y=x√√9-x² 3 x
> Use substitutions and the fact that a circle of radius r has area πr2 to evaluate the following integrals. ∫-6 0√ (-x2 - 6x) dx
> Use substitutions and the fact that a circle of radius r has area πr2 to evaluate the following integrals. ∫0 √2 √ (4 - x4) * 2x dx
> Use substitutions and the fact that a circle of radius r has area πr2 to evaluate the following integrals. ∫-π/2 π/2 √(1 - sin2 x) cos x dx
> Evaluate the following definite integrals. ∫0 π/2 sin(2x – π/2) dx
> Evaluate the following definite integrals. ∫0 1 x sin πx dx
> Determine the integrals by making appropriate substitutions. ∫ xex2 dx
> Evaluate the following definite integrals. ∫0 π/4 tan x dx
> Evaluate the following definite integrals. ∫0 π esin x cos x dx
> Evaluate the following definite integrals. ∫1 e ln x dx
> Evaluate the following definite integrals. ∫1 e ln x / x dx
> Evaluate the following definite integrals. ∫-1 12xex dx
> Evaluate the following definite integrals. ∫1 3 x2ex3 dx
> Evaluate the following definite integrals. ∫0 4 8x (x + 4)-3 dx
> Evaluate the following definite integrals. ∫0 1 x / (x2 + 3) dx
> Evaluate the following definite integrals. ∫0 1 (2x - 1) (x2 - x)10 dx
> Evaluate the following definite integrals. ∫-1 2 (x2 – 1) (x3 - 3x)4 dx
> Determine the integrals by making appropriate substitutions. ∫ (x3 - 6x)7 (x2 - 2) dx
> Determine the integrals by making appropriate substitutions. ∫ 2x(x2 + 4)5 dx
> Maria and Tracey became good friends while working at the same entity. Two years ago, they both decided to increase their savings so that they could eventually purchase homes. Each began by putting a portion of each month’s salary into a savings account.
> Budget Cupboards produces kitchen and bathroom cupboards that incorporate unusual functions, such as specialty drawers for knives and kitchen tools, and kitchen appliance holders that pop up from under the counter top. Competition in this industry has re
> Humphrey Manufacturing produces car parts and batteries. All direct materials are added at the beginning of production, and conversion costs are incurred evenly throughout production. The following production information is for the month of April: Requ
> Refer to the information presented in Exercise 8.17 Required Prepare a process cost report under the FIFO method for December. Exercise 8.17: Fox and Sons is a toy maker and produces Flying Flingbats, a soft foam rubber boomerang. All direct materials
> Refer to the information presented in Exercise 8.17 Required Using the FIFO method, prepare a schedule calculating the cost per equivalent unit for April. Exercise 8.17: Fox and Sons is a toy maker and produces Flying Flingbats, a soft foam rubber boom
> Refer to the information presented in Exercise 8.17. Required Prepare a process cost report under the weighted average method for December. Exercise 8.17: Fox and Sons is a toy maker and produces Flying Flingbats, a soft foam rubber boomerang. All dire
> Fox and Sons is a toy maker and produces Flying Flingbats, a soft foam rubber boomerang. All direct materials are added at the beginning of production, and conversion costs are incurred evenly throughout production. Conversion was 75 per cent complete fo
> Fine Fans mass-produces small electric fans in Hawley Beach for home use. All direct materials are added at the beginning of production, and conversion costs are incurred evenly throughout production. The following production information is for the month
> Francisco’s mass-produces folding chairs in Port Sorrell. All direct materials are added at the beginning of production, and conversion costs are incurred evenly throughout production. The following production information is for the mon
> Jones Company manufactures custom doors. When job 186 (a batch of 14 custom doors) was being processed in the machining department, one of the wood panels on a door split. This problem occurs periodically and is considered normal spoilage. Direct materia
> Identify two key influences on the nature of a management accounting system.
> At the beginning of the accounting period, the accountant for ABC Industries estimated that total overhead would be $80 000. Overhead is allocated to jobs on the basis of direct labour cost. Direct labour was budgeted to cost $200 000 this period. During
> The Futons for You Company sells batches of custom-made futons to customers and uses predetermined rates for fixed overhead, based on machine hours. The following data are available for last year: Required (a) Calculate the estimated overhead allocatio
> Vern’s Van Service customises light trucks according to customers’ orders. This month the entity worked on five jobs, numbered 207 to 211. Materials requisitions for the month were as follows: An analysis of the payr
> Rebecca Ltd is a manufacturer of machines made to customer specifications. All production costs are accumulated by means of a job order costing system. The following information is available at the beginning of the month of October. A review of the job
> Langley uses a job costing system. At the beginning of the month of June, two orders were in process as follows: There was no inventory in finished goods on 1 June. During June, orders numbered 106 to 120 were put into process. Direct materials require
> Jasper Company uses a job costing system. Overhead is allocated based on 120 per cent of direct labour cost. Last month’s transactions in the work in process account are shown here: Only one job, number 850, was still in process at th
> Job 87M had direct material costs of $400 and a total cost of $2100. Overhead is allocated at the rate of 75 per cent of prime cost (direct material and direct labour). Required (a) How much direct labour was used? (b) How much overhead was allocated?
> Franklin Fabrication produces custom-made security doors and gates. Currently two jobs are in process, 359 and 360. During production of Job 359, the supervisor was on holidays and the employees made several errors in cutting the metal pieces for the two
> Shane’s Shovels produces small, custom earth-moving equipment for landscaping companies. Manufacturing overhead is allocated to work in process using an estimated overhead rate. During April, transactions for Shane’s S
> One Glass Brewery estimates the following activity for the coming year: At the end of the financial period the following information was collected: Required (a) What was the predetermined manufacturing overhead rate calculated at the beginning of t
> Outline the meaning of structural cost drivers.
> A college student, Brad Worth, plans to sell atomic alarm clocks with CD players over the internet and by mail order to help pay his expenses during the summer semester. He buys the clocks for $32 and sells them for $50. If payment by check accompanies t
> Play Time Toys is organised into two major divisions: marketing and production. The production division is further divided into three departments: puzzles, dolls and video games. Each production department has its own manager. The entityâ€
> Maryborough Manufacturing has projected sales in units for four months of operations as follows: The product sells for $18 per unit. Twenty-five per cent of the customers are expected to pay in the month of sale and take a 3 per cent discount; 70 per c
> The Zel Company operates at local flea markets. It has budgeted the following sales for the indicated months. Zel’s success in this specialty market is due in large part to the extension of credit terms and the budgeting techniques im
> Ken Martin, manager of Lonnie Car Repairers, has requested that you prepare a cash budget for the months of December and January. He has provided the following information to assist in this task. * Projected cash balance at the end of November is $30 000
> Organic Industries intends to start business on the first of January. Production plans for the first four months of operations are as follows: Each unit requires 2 kilograms of material. The entity would like to end each month with enough raw material
