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study help
mathematics
precalculus
Calculus Early Transcendentals 8th edition James Stewart - Solutions
Solve the differential equation.y' = x - y
Solve the differential equation.y' - y = ex
Solve the differential equation.y' + y = 1
Determine whether the differential equation is linear.dR/dt + t cos R = e-t
Determine whether the differential equation is linear. ue' =t + Jt du dt
Determine whether the differential equation is linear.y' - x = y tan x
Determine whether the differential equation is linear.y' + x√y = x2
The table gives the midyear population of Norway, in thousands, from 1960 to 2010.Use a calculator to fit both an exponential function and a logistic function to these data. Graph the data points and both functions, and comment on the accuracy of the models. Year Population Year Population 1990
The table gives the midyear population of Japan, in thousands, from 1960 to 2010.Use a calculator to fit both an exponential function and a logistic function to these data. Graph the data points and both functions, and comment on the accuracy of the models. Year Population Year Population 1960
(a) Show that if P satisfies the logistic equation (4), then(b) Deduce that a population grows fastest when it reaches half its carrying capacity. 2P d?P k*P = k²P[ 1 dt?
(a) Assume that the carrying capacity for the US population is 800 million. Use it and the fact that the population was 282 million in 2000 to formulate a logistic model for the US population.(b) Determine the value of k in your model by using the fact that the population in 2010 was 309
The population of the world was about 6.1 billion in 2000. Birth rates around that time ranged from 35 to 40 million per year and death rates ranged from 15 to 20 million per year. Let’s assume that the carrying capacity for world population is 20 billion.(a) Write the logistic differential
Suppose a population P(t) satisfies dP/dt = 0.4P - 0.001P2 P(0) = 50 where t is measured in years.(a) What is the carrying capacity?(b) What is P'(0)?(c) When will the population reach 50% of the carrying capacity?
A population grows according to the given logistic equation, where t is measured in weeks.(a) What is the carrying capacity? What is the value of k?(b) Write the solution of the equation.(c) What is the population after 10 weeks?dP/dt = 0.0P - 0.0004P2, P(0) = 40
A population grows according to the given logistic equation, where t is measured in weeks.(a) What is the carrying capacity? What is the value of k?(b) Write the solution of the equation.(c) What is the population after 10 weeks?dP/dt = 0.04P(1 -P/1200), P(0) = 60
(a) If f is continuous, prove that(b) Use part (a) to evaluate
Use Exercise 92 to evaluate the integral X sin x п dx Jo 1 + cos?x cosʻx
If f is continuous on [0, π], use the substitution u = π - x to show that |" xf(sin x) dx |" f(sin x) dx 2 Jo TT
If a and b are positive numbers, show that
If f is continuous on R, prove that
If f is continuous on R, prove that For the case where f (x) > 0 and 0 < a < b, draw a diagram to interpret this equation geometrically as an equality of areas. Lf-9) dx = [,1(0)dx (-x) dx =
If f is continuous and '3 f(x) dx = 4, find xf(x²) dx.
If f is continuous and [ F(x) dx = 10, find f(2x) dx.
Alabama Instruments Company has set up a production line to manufacture a new calculator. The rate of production of these calculators after t weeks is(That production approaches 5000 per week as time goes on, but the initial production is lower because of the workers’ unfamiliarity with the
Dialysis treatment removes urea and other waste products from a patient’s blood by diverting some of the bloodflow externally through a machine called a dialyzer. The rate at which urea is removed from the blood (in mg/min) is often well described by the equationwhere r is the rate of flow of
The rate of growth of a fish population was modeled by the equation where t is measured in years and G in kilograms per year. If the biomass was 25,000 kg in the year 2000, what is the predicted biomass for the year 2020? 60,000e -0.6t -0.6t G(1) (1 + 5e-0.6t)2
Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhalation takes about 5 s. The maximum rate of air flow into the lungs is about 0.5 L/s. This explains, in part, why the function has often been used to model the rate of air flow into the lungs. Use
A bacteria population starts with 400 bacteria and grows at a rate of bacteria per hour. How many bacteria will there be after three hours? |(1) = (450.268)e1.125671|
A model for the basal metabolism rate, in kcal/h, of a young man is R(t) = 85 - 0.18 cos(t/12), where t is the time in hours measured from 5:00 am. What is the total basal metabolism of this man, ʃ240 R(t) dt, over a 24-hour time period?
Evaluate by making a substitution and interpreting the resulting integral in terms of an area. SoxV1 – x4 dx
Evaluate by writing it as a sum of two integrals and interpreting one of those integrals in terms of an area. L, (x + 3)/4 – x² dx -2
Use a graph to give a rough estimate of the area of the region that lies under the given curve. Then find the exact area. y = 2 sin x - sin 2x, 0 < x < π
Use a graph to give a rough estimate of the area of the region that lies under the given curve. Then find the exact area. = 2x + 1, 0
Verify that f (x) = sin 3√x is an odd function and use that fact to show that sin Vx dx < 1 -2
Evaluate the definite integral. dx (1 + Jx)* 4
Evaluate the definite integral. *т/2 (T/2 sin(27t/T – a) dt a) dt
Evaluate the definite integral. ci e² + 1 dz Jo e² + z
Evaluate the definite integral. '2 (x – 1)e«-1)² dx
Evaluate the definite integral. dx e4 X VIn x
Evaluate the definite integral. '4 dx 1 + 2x
Evaluate the definite integral. xVx- 1 dx
Evaluate the definite integral. *T/3 x* sin x dx |-1/3
Evaluate the definite integral. (a > 0) x² + a² dx
Evaluate the definite integral.
Evaluate the definite integral. dx C13 V(1 + 2x)? 3
Evaluate the definite integral. *T/2 cos x sin(sin x) dx
Evaluate the definite integral. (T/4 (x³ + x* tan x) dx J-7/4
Evaluate the definite integral. хе dx Jo
Evaluate the definite integral. ,1/х (2 e/x dx x?
Evaluate the definite integral. *2п/3 csc? (1) dt Уп/3
Evaluate the definite integral. *7/6 sin t - dt cos't Jo
Evaluate the definite integral. dx Jo 5x + 1
Evaluate the definite integral. V1 + 7x dx
Evaluate the definite integral. | (3t – 1)50 dt
Evaluate the definite integral. | cos(Tt/2) dt Jo
Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take C = 0). sin x costx dx
Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take C = 0). cos x sin x dx
Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take C = 0). tan?0 sec?0 de
Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take C = 0). | x(x? – 1)° dx dx
Evaluate the indefinite integral. SrV?? + I dx -2
Evaluate the indefinite integral. | x(2x + 5)° dx
Evaluate the indefinite integral. Jr*/2 + x dx
Evaluate the indefinite integral. dx
Evaluate the indefinite integral. dx 4 1 +
Use a graph to give a rough estimate of the area of the region that lies under the curve y = x√x, 0 ≤ x ≤ 4. Then find the exact area.
Evaluate the indefinite integral. cos(In t) dt
Evaluate the indefinite integral. J cot x dx
Evaluate the indefinite integral. sin x – dx 1 + cos?x
Evaluate the indefinite integral. sin 2x –dx 1 + cos?x
Evaluate the indefinite integral. dt cos?t /1 + tan t
Evaluate the indefinite integral. cosh x dx | sinh²x
Evaluate the indefinite integral. 2' dt 2' + 3
Evaluate the indefinite integral. cot x csc?x dx
Evaluate the indefinite integral. cos(T/x) dx
Evaluate the indefinite integral. cos (1 + 5t) dt
Evaluate the indefinite integral. (arctan x)? dx x? + 1 .2
Evaluate the indefinite integral. (arctan x)? dx x² + 1
Evaluate the indefinite integral. sec?x dx 2. tan?x
Evaluate the indefinite integral. | 5' sin(5') dt
Evaluate the indefinite integral. cos t sin sin t dt
Evaluate the indefinite integral. (х? + 1)(х3 + 3х)* dx Зх)* dx
Evaluate the indefinite integral. dx (a + 0) ах + b
Evaluate the indefinite integral. Je*/1+ e² dx
Evaluate the indefinite integral. 2 dx [fxVx+ x /x + 2 dx
Evaluate the indefinite integral. | sec?0 tan³0 d0
Evaluate the indefinite integral. sin x sin(cos x) dx
Evaluate the indefinite integral. (In x)? dx х
Evaluate the indefinite integral. dz z' + 1 .3
Evaluate the indefinite integral. a + bx² dx Зах + bx3
Evaluate the indefinite integral. sin Vr x,
Evaluate the indefinite integral.
Evaluate the indefinite integral. Je-Sr dr -5r
Evaluate the indefinite integral. y²(4 – y³)/³ dy
Evaluate the indefinite integral. dx 5 — Зх
Evaluate the indefinite integral. | sec2 20 de
Evaluate the indefinite integral. cos'0 sin 0 de cOs
Evaluate the indefinite integral. cos(Tt/2) dt
Evaluate the indefinite integral. fre'dx e*dx
Evaluate the indefinite integral. || xVI - x² dx
Evaluate the integral by making the given substitution. | V2t + 1 dt, u= 2t + 1
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