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mathematics
applied calculus
Calculus And Its Applications 14th Edition Larry Goldstein, David Lay, David Schneider, Nakhle Asmar - Solutions
If f (s, t) = t sin st, find af ძs and af dt
Find the area under the curve y = cos t from t = 0 to t = π/2.
The basal metabolism (BM) of an organism over a certain time period may be described as the total amount of heat in kilocalories (kcal) that the organism produces during this period, assuming that the organism is at rest and not subject to stress. The basal metabolic rate (BMR) is the rate in kcal
Find the area under the curve y = sin 2t from t = 0 to t = π/4.
The average weekly temperature in Washington, D.C., t weeks after the beginning of the year isThe graph of this function is sketched in Fig. 12.(a) What is the average weekly temperature at week 18?(b) At week 20, how fast is the temperature changing?(c) When is the average weekly temperature 39
A person’s blood pressure P at time t (in seconds) is given by P = 100 + 20 cos 6t.(a) Find the maximum value of P (called the systolic pressure) and the minimum value of P (called the diastolic pressure) and give one or two values of t where these maximum and minimum values of P occur.(b) If
The number of hours of daylight per day in Washington, D.C., t weeks after the beginning of the year isThe graph of this function is sketched in Fig. 13.(a) How many hours of daylight are there after 42 weeks?(b) After 32 weeks, how fast is the number of hours of daylight decreasing?(c) When is
Find the equation of the line tangent to the graph of y = tan t at t = π/4.
Sketch the graph of f (t) = sin t + cos t for -2π ≤ t ≤ 2p, using the following steps:(a) Find all t between -2π and 2π such that f′(t) = 0. Plot the corresponding points on the graph of y = f (t).(b) Check the concavity of f (t) at the points in part (a). Make sketches of the graph near
Sketch the graph of y = t + sin t for 0 ≤ t ≤ 2π.
In Fig. 2:Find the shaded area A1. Y 0 A₁ Figure 2 cos x Td4 TV2 Ag sin x T Xx
In Fig. 2:Find the shaded area A2. Y 0 A₁ Figure 2 cos x Td4 TV2 Ag sin x T Xx
Find the area under the curve y = 2 + sin 3t from t = 0 to t = π/2.
In Fig. 2:Find the shaded area A3. Y 0 A₁ Figure 2 cos x Td4 TV2 Ag sin x T Xx
Find the area of the region between the curve y = sin t and the t-axis from t = 0 to t = 2π.
In Fig. 2:Find the shaded area A4. Y 0 A₁ Figure 2 cos x Td4 TV2 Ag sin x T Xx
Find the area of the region between the curve y = cos t and the t-axis from t = 0 to t = 3π/2.
Find the average of the function f (t) over the given interval. f(t) = 1 + sin 2t −cos 2t, 0 ≤ t ≤ 2π
Find the area of the region bounded by the curves y = x and y = sin x from x = 0 to x = π.
Find the average of the function f (t) over the given interval. f(t) = t - cos 2t, 0≤ t ≤ TT
Find the average of the function f (t) over the given interval. f(t) = 1000 + 200 sin 2 (t - 4), 0 sts Зп 4
Find the average of the function f (t) over the given interval. f(t) = cost + sin t, -T≤ t ≤0
Determine the integrals in Exercises by making appropriate substitutions. √2x(x² + 2x(x² + 4)5 dx
Determine the following indefinite integrals: [x x sin 3x² dx
Determine the integrals in Exercises by making appropriate substitutions. [2(2x 2(2x - 1)7 dx
Find the present value of a continuous stream of income over 5 years when the rate of income is constant at $35,000 per year and the interest rate is 7%.
Determine the following indefinite integrals: S √2x + 1 dx
Describe integration by substitution in your own words.
Determine if the given expression approaches a limit as b → ∞, and find that number when it does.5/b
Determine the integrals in Exercises by making appropriate substitutions. 2x + 1 √x²+x+3 dx
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
A continuous stream of income is being produced at the constant rate of $60,000 per year. Find the present value of the income generated during the time from t = 2 to t = 6 years, with a 6% interest rate.
Determine the following indefinite integrals: x(1 - 3x²)5 dx
Describe integration by parts in your own words.
Determine the following indefinite integrals: (In x)5 S X - dx
Determine if the given expression approaches a limit as b → ∞, and find that number when it does.b2
Determine the integrals in Exercises by making appropriate substitutions. f (x² + 2x + 3)(x + 1)d
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
Determine if the given expression approaches a limit as b → ∞, and find that number when it does. 1 b 3
Find the present value of a continuous stream of income over the time from t = 1 to t = 5 years when the interest rate is 10% and the income is produced at the rate of $12,000 per year.
Determine the following indefinite integrals: z(x up). [ X dx
Describe the change of limits rule for the integration by substitution of a definite integral.
Determine if the given expression approaches a limit as b → ∞, and find that number when it does.-3e2b
Divide the interval into n subintervals and list the value of Δx and the midpoints x1,....,xn of the subintervals.-1 ≤ x ≤ 1; n = 4
Determine the integrals in Exercises by making appropriate substitutions. √3x²(x²-1), dx
Find the present value of a continuous stream of income over 4 years if the rate of income is 25 e-0.02t thousand dollars per year at time t and the interest rate is 8%.
Determine the following indefinite integrals: 1 √4x + 3 S dx
State the formula for the integration by parts of a definite integral.
Determine the integrals in Exercises by making appropriate substitutions. 2xe-x² dx 2 v
Determine if the given expression approaches a limit as b → ∞, and find that number when it does. 1 2 b
Determine if the given expression approaches a limit as b → ∞, and find that number when it does. 4 6² 2 b
Divide the interval into n subintervals and list the value of Δx and the midpoints x1,....,xn of the subintervals.0 ≤ x ≤ 3; n = 6
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. Y 50 40 30 20 10 سر 0 1 2 3 4 5 6 7 8 Figure 11
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%.
Refer to the graph in Fig. 11. Apply the trapezoidal rule with n = 4 to estimate the area under the curve. Y 50 40 30 20 10 012 Figure 11 H 34 5 6 7 8 X
State the midpoint rule. (Include the meaning of all symbols used.)
Determine the following indefinite integrals: fxV4-x² d. dx
Determine the integrals in Exercises by making appropriate substitutions. fxV4-x² d. dx
State the trapezoidal rule. (Include the meaning of all symbols used.)
A continuous stream of income is produced at the rate of 20 e1-0.09t 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 to t = 5 years.(b) Compute the present value
Explain the formula S = 2M + T 3
Determine the integrals in Exercises by making appropriate substitutions. dx ε(x u[ + I)
Approximate the following integrals by the midpoint rule; then, find the exact value by integration. Express your answers to five decimal places. f (x² + 5)dx; n = 2,4 2
Determine the following indefinite integrals: [x x sin 3x dx
Determine the following indefinite integrals: x²e-x³ 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 the company’s earnings over the next 2
Determine if the given expression approaches a limit as b → ∞, and find that number when it does.2 - (b + 1)-1/2
Approximate the following integrals by the midpoint rule; then, find the exact value by integration. Express your answers to five decimal places. La (x - 1)² dx; n = 2,4
Determine the integrals in Exercises by making appropriate substitutions. 1 √2x + 1 dx
Determine the following indefinite integrals: x ln(x² + 1) 2 x² + 1 xp.
State the error of approximation theorem for each of the three approximation rules.
Determine if the given expression approaches a limit as b → ∞, and find that number when it does.5 - (b - 1)-1
Approximate the following integrals by the midpoint rule; then, find the exact value by integration. Express your answers to five decimal places. So ex dx; n = 5
Determine the integrals in Exercises by making appropriate substitutions. f(x³3-6 - 6x)7(x² - 2)dx
In 2012, the population density of a city t miles from the city center was 120 e-0.65t thousand people per square mile.(a) Write a definite integral whose value equals the number of people (in thousands) who lived within 5 miles of the city center.(b) Calculate the definite integral in part (a).
State the formula for each of the following quantities:(a) Present value of a continuous stream of income(b) Total population in a ring around the center of a city
Determine if the given expression approaches a limit as b → ∞, and find that number when it does.5(b2 + 3)-1
Approximate the following integrals by the midpoint rule; then, find the exact value by integration. Express your answers to five decimal places. जि 1 x + 1 - dx; n = 5
Determine the following indefinite integrals: [x² x² cos 3x dx
Approximate the following integrals by the trapezoidal rule; then, find the exact value by integration. Express your answers to five decimal places. √ √(x - 2)² dx; n = 4
Determine the integrals in Exercises by making appropriate substitutions. Liter² xe हर dx
Determine the following indefinite integrals: In(ln x) [the x ln x xp.
Use the population density from Exercise 9 to calculate the number of people who lived between 3 and 5 miles from the city center.
How do you determine whether an improper integral is convergent?
Determine if the given expression approaches a limit as b → ∞, and find that number when it does.4(1 - b-3/4)
Determine the integrals in Exercises by making appropriate substitutions. f= V X dx
Determine the following indefinite integrals: [₁ In x² dx
The population density of Philadelphia in 1940 was given by the function 60 e-0.4t. Calculate the number of people who lived within 5 miles of the city center. Sketch the graphs of the population densities for 1900 and 1940 on a common graph. What trend do the graphs exhibit?
Determine if the given expression approaches a limit as b → ∞, and find that number when it does.e-b/2 + 5
Approximate the following integrals by the trapezoidal rule; then, find the exact value by integration. Express your answers to five decimal places. 1 4 x-3 -dx; n = 5
Determine the integrals in Exercises by making appropriate substitutions. "In(2x) S™ X - dx
Determine the following indefinite integrals: x√x + 1 dx
Suppose that the population density function for a city is 40e-0.5t thousand people per square mile. Let P(t) be the total population that lives within t miles of the city center, and let Δt be a small positive number.(a) Consider the ring about the city whose inner circle is at t miles and outer
A volcano erupts and spreads lava in all directions. The density of the deposits at a distance t kilometers from the center is D (t) thousand tons per square kilometer, where D (t) = 11(t2 + 10)-2. Find the tonnage of lava deposited between the distances of 1 and 10 kilometers from the center.
Determine if the given expression approaches a limit as b → ∞, and find that number when it does.2 - e-3b
Approximate the following integrals by the trapezoidal rule; then, find the exact value by integration. Express your answers to five decimal places. [²/3 dx= 1 x انا 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 J-1 2x dx; n = 2,4
Determine the following indefinite integrals: J X √3x - 1 dx
Determine the integrals in Exercises by making appropriate substitutions. Vln x X dx
Determine the integrals in Exercises by making appropriate substitutions. .4 X 5 x² + 1 dx
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