Determine the integrals by making appropriate substitutions. ∫ x √(4 - x2)dx
> For the cash flows shown, find the future worth in (a) year 5, and (b) year 4. Assume an i of 10% per year. Year Cash Flow, $ 0 1 0 0 2 3 4 3000 3000 3000 5 3000
> A manufacturer of industrial grade gas handling equipment wants to have $500,000 in an equipment replacement contingency fund 10 years from now. If the company plans to deposit a uniform amount of money each year beginning now and continuing through year
> How much money would be accumulated 18 years from now from deposits of $15,000 per year for five consecutive years, starting 3 years from now, if the interest rate is 8% per year?
> Calculate the equivalent future cost in year 10 for the following series of disbursements at an interest rate of 10% per year. Also, write a single-cell spreadsheet function that will determine the future worth. Year 01234 4 Disbursement, $ Year 5 6
> Abby purchased 100 shares of her dad’s favorite stock for $25.80 per share exactly 1 year ago, commission free. She sold it today for a total amount of $2865. She plans to invest the entire amount in a different corporation’s stock today, but must now pa
> Lifetime Savings Accounts, known as LSAs, allow people to invest after-tax money without being taxed on any of the gains. If an engineer invests $10,000 now and $10,000 each year for the next 20 years, how much will be in the account immediately after th
> Kenworth Imaging got a $700,000 loan that came with a choice of two different repayment schedules. In Plan 1, the company would have to repay the loan in 4 years with four equal payments at an interest rate of 10% per year. In Plan 2, the company would r
> A maker of micromechanical systems can reduce product recalls by 10% with the installation of new packaging equipment. If the cost of the new equipment is expected to be $40,000 four years from now, how much could the company afford to spend now (instead
> An entrepreneurial electrical engineer has approached a large utility with a proposal that promises to reduce the utility’s power bill by at least 15% per year for the next 5 years through installation of patented surge protectors. The proposal states th
> The operating cost for a pulverized coal cyclone furnace is expected to be $80,000 per year. The steam produced will be needed for only 6 years beginning now (i.e., years 0 through 5). What is the equivalent annual worth in years 1 through 5 of the opera
> How much will Kingston Technologies have to pay each year in eight equal payments, starting 2 years from now, to repay a $900,000 loan? The interest rate is 8% per year.
> Improvised explosive devices (IEDs) are responsible for many deaths in times of strife and war. Unmanned ground vehicles (robots) can be used to disarm the IEDs and perform other tasks as well. If the robots cost $140,000 each and the Military Arms Unit
> The net cash flows associated with development and sale of a new product are shown. Determine the beginning of period annual worth (i.e., for years 0 through 5) at an interest rate of 12% per year. The cash flows are in $1000 units. Year 12 3 4 5 6 C
> What is the equivalent annual cost in years 1 through 7 of a contract that has a first cost of $70,000 in year 0 and annual costs of $15,000 in years 3 through 7? Use an interest rate of 10% per year.
> The Gap has some of its jeans stone-washed under a contract with Vietnam Garment Corporation (VGC). If VGC’s estimated operating cost per machine is $26,000 for year 1 and it increases by $1500 per year through year 5, the equivalent uniform annual cost
> How much could BTU Oil & Gas Fracking afford to spend on new equipment each year for the next 3 years if it expects a profit of $50 million 3 years from now? Assume the company’s MARR is 20% per year.
> The first mass produced automobile was the Ford Model T, initially manufactured and sold in 1909 for $825. The rate of inflation in the United States over the period 1909 to 2015 has averaged 3.10% per year. You just purchased a new car for $28,000. You
> Evaluate the following definite integrals. ∫0 11 / (1 + 2x)4 dx
> Evaluate the following definite integrals. ∫3 5 x √(x2 – 9) dx
> Evaluate the following definite integrals. ∫0 1 x (3 + x)5 dx
> Evaluate the following definite integrals. ∫0 3 x / (2x + 1) dx
> Evaluate the following definite integrals. ∫0 1 2x / √(x2 + 1) dx
> Evaluate the following integrals: ∫ x / ex dx
> Evaluate the following integrals: ∫ x (2x - 3)2 dx
> Evaluate the following integrals: ∫ x (x + 7)4 dx
> Evaluate the following integrals: ∫ x ex/2 dx
> Evaluate the following integrals: ∫ x e5x dx
> Determine the integrals by making appropriate substitutions. ∫ 1/√(2x + 1) dx
> Evaluate ∫x7 ex4 dx.
> Evaluate ∫x ex (x + 1)2 dx using integration by parts.
> Figure 2 shows graphs of several functions f (x) whose slope at each x is x / ex/3. Find the expression for the function f (x) whose graph passes through (0, 6). Figure 2: ม (0, 6)
> Figure 1 shows graphs of several functions f (x) whose slope at each x is x/√(x + 9). Find the expression for the function f (x) whose graph passes through (0, 2). Figure 1: Y (0, 2)
> Evaluate the following integrals using techniques studied thus far. ∫ (x2 - x sin 2x) dx
> Evaluate the following integrals using techniques studied thus far. ∫ (x ex2 - 2x) dx
> Evaluate the following integrals using techniques studied thus far. ∫ (x3/2 + ln 2x) dx
> Evaluate the following integrals using techniques studied thus far. ∫ (x e2x + x2) dx
> Evaluate the following integrals using techniques studied thus far. ∫ ln x / x5 dx
> Evaluate the following integrals using techniques studied thus far. ∫ x sec2 (x2 + 1) dx
> Determine the integrals by making appropriate substitutions. ∫ (1 + ln x)3 / x dx
> Evaluate the following integrals using techniques studied thus far. ∫ (ln x)5 / x dx
> Evaluate the following integrals using techniques studied thus far. ∫ (3x + 1) ex/3 dx
> Evaluate the following integrals using techniques studied thus far. ∫ 4x cos (x + 1) dx
> Evaluate the following integrals using techniques studied thus far. ∫ x (x2 + 5)4 dx
> Evaluate the following integrals using techniques studied thus far. ∫ 4x cos (x2 + 1) dx
> Evaluate the following integrals using techniques studied thus far. ∫ x (x + 5)4 dx
> Evaluate the following integrals: ∫ ln √(x + 1) dx
> Evaluate the following integrals: ∫ x2 e-x dx
> Evaluate the following integrals: ∫ ln (ln x) / x dx
> Evaluate the following integrals: ∫ ln x4 dx
> Evaluate the following integrals: ∫ x-3 ln x dx
> Evaluate the following integrals: ∫ x ln 5x dx
> Evaluate the following integrals: ∫ x sin 8x dx
> Evaluate the following integrals: ∫ x cos x dx
> Evaluate the following integrals: ∫ x5 ln x dx
> Evaluate the following integrals: ∫ √x ln √x dx
> Evaluate the following integrals: ∫ x √(2 – x) dx
> Evaluate the following integrals: ∫ x √(x + 1) dx
> Evaluate the following integrals: ∫ (x + 2) / e2x dx
> Evaluate the following integrals: ∫ 6x /e3x dx
> Determine the integrals by making appropriate substitutions. ∫ 2xe-x2 dx
> Evaluate the following integrals: ∫ (1 + x)2 e2x dx
> Evaluate the following integrals: ∫ e2x (1 - 3x) dx
> Evaluate the following integrals: ∫ x / √(3 + 2x) dx
> Evaluate the following integrals: ∫ x / √(x + 1) dx
> Evaluate the following integrals: ∫ x2 ex dx
> Determine ∫ 2x (x2 + 5) dx by making a substitution. Then, determine the integral by multiplying out the integrand and antidifferentiating. Account for the difference in the two results.
> Determine the following integrals by making an appropriate substitution. ∫ tan x sec2 x dx
> Determine the following integrals by making an appropriate substitution. ∫ (sin x + cos x) / (sin x - cos x) dx
> Determine the following integrals by making an appropriate substitution. ∫cot x dx
> Determine the following integrals by making an appropriate substitution. ∫ cos 3x / (12 - sin 3x) dx
> Determine the integrals by making appropriate substitutions. ∫ 3x2e(x3-1) dx
> Determine the following integrals by making an appropriate substitution. ∫ (sin 2x) ecos 2x dx
> Determine the following integrals by making an appropriate substitution. ∫cos3 x sin x dx
> Determine the following integrals by making an appropriate substitution. ∫cos x / (2 + sin x)3 dx
> Determine the following integrals by making an appropriate substitution. ∫cos √x / √x dx
> Determine the following integrals by making an appropriate substitution. ∫ 2x cos x2 dx
> Determine the following integrals by making an appropriate substitution. ∫sin x cos x dx
> Determine the following integrals using the indicated substitution. ∫ (1 + ln x) sin(x ln x)dx; u = x ln x
> Determine the following integrals using the indicated substitution. ∫ x sec2 x2 dx; u = x2
> Determine the following integrals using the indicated substitution. ∫ x4 / (x5 – 7) ln(x5 - 7) dx; u = ln(x5 - 7)
> Determine the following integrals using the indicated substitution. ∫ (x + 5)-1/2 e√(x+5) dx; u = √(x+5)
> Determine the integrals by making appropriate substitutions. ∫ (x2 + 2x + 3)6(x + 1) dx
> Figure 2 shows graphs of several functions f (x) whose slope at each x is (2√x + 1)/ √x. Find the expression for the function f (x) whose graph passes through (4, 15). Figure 2: 15 10 5 0 Y 2 (4, 15) 4
> Figure 1 shows graphs of several functions f (x) whose slope at each x is x/√(x2 + 9). Find the expression for the function f (x) whose graph passes through (4, 8). Figure 1: 1 16+ 0 (4,8) 2 4 6 8
> Determine the integral by making appropriate substitutions. ∫ (e2x - 1) / (e2x + 1) dx
> Determine the integral by making appropriate substitutions. ∫ 1 / (1 + ex) dx
> Determine the integral by making appropriate substitutions. ∫ (1 + e-x)3 / ex dx
> Determine the integral by making appropriate substitutions. ∫ (ex + e-x) / (ex - e-x) dx
> Determine the integral by making appropriate substitutions. ∫ (ex + e-x) / (ex - e-x) dx
> Determine the integral by making appropriate substitutions. ∫ ex / (1 + 2ex) dx
> Determine the integral by making appropriate substitutions. ∫ ex √(1 + ex) dx
> Determine the integrals by making appropriate substitutions. ∫ ex (1 + ex)5 dx
> Determine the integrals by making appropriate substitutions. ∫ (2x + 1)/ √(x2 + x + 3) dx
> Determine the following indefinite integrals: ∫ x(1 - 3x2)5 dx
> Determine the following indefinite integrals: ∫ √(2x + 1) dx
> Determine the integrals by making appropriate substitutions. ∫ dx / (3 - 5x)
> Determine the following indefinite integrals: ∫ x sin 3x2 dx
> The capitalized cost of an asset is the total of the original cost and the present value of all future “renewals” or replacements. This concept is useful, for example, when you are selecting equipment that is manufactured by several different companies.
> Suppose that a machine requires daily maintenance, and let M(t) be the annual rate of maintenance expense at time t. Suppose that the interval 0 ≤ t ≤ 2 is divided into n subintervals, with endpoints t0 = 0, t1, … , tn = 2. (a) Give a Riemann sum that ap
> Suppose that t miles from the center of a certain city the property tax revenue is approximately R(t) thousand dollars per square mile, where R(t) = 50 e-t/20. Use this model to predict the total property tax revenue that will be generated by property wi
