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mathematics
precalculus

Questions and Answers of Precalculus

Use Simpson’s Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by a calculator.y = 3√x, 1 < x < 6
Use Simpson’s Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produced by a calculator.y = x sin x, 0 < x < 2π
Graph the curve and visually estimate its length. Then use your calculator to find the length correct to four decimal places. y = x + cos x, 0 < x < π/2
Graph the curve and visually estimate its length. Then use your calculator to find the length correct to four decimal places.y = x2 + x3, 1 < x < 2
Find the length of the arc of the curve from point P to point Q.x2 = (y - 4)3, p(1,5), Q(8, 8)
Find the exact length of the curve.y = 1 - e-x, 0 < x < 2
Find the exact length of the curve.y = In(1 - x2), 0 < x < 1/2
Find the exact length of the curve.y = √x - x2 + sin-1 (√x)
Find the exact length of the curve.y = 1/4x2 - 1/2In x, 1 < x < 2
Find the exact length of the curve.y = 3 + 1/2cosh 2x, 0 < x < 1
Find the exact length of the curve.y = In(sec x), 0 < x < π/4
Find the exact length of the curve. y = In(cos x), 0 < x < π/3
Find the exact length of the curve.x = y4/8 + 1/4y2, 1 < y < 2
Find the exact length of the curve.36y2 = (x2 - 4)2, 2 < x < 3, y > 0
Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.y2 = In x, -1 < y < 1
Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.x = √y - y, 1 < y < 4
Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.x = y2 - 2y, 0 < y < 2
Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.y = x - In x, 1 < x < 4
Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.y = xe-x, 0 < x < 2
Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.y = sin x, 0 < x < π
If f' is continuous on [0, ∞) and show that |lim, f(x) = 0, f'(x) dx = -f(0)
Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule with n = 10 to approximate the given integral.Round your answers to six decimal places. Vx cos x dx 1
Use (a) the Trapezoidal Rule, (b) the Midpoint Rule, and (c) Simpson’s Rule with n = 10 to approximate the given integral.Round your answers to six decimal places. 1 dx 2 In x
Use the Table of Integrals on the Reference Pages to evaluate the integral. cos x V4 + sin²x dx
Use the Table of Integrals on the Reference Pages to evaluate the integral. /4x2 — 4х — 3 dx
Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take C = 0). dx Vx2 + 1
Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take C = 0). In(x² + 2x + 2) dx
Evaluate the integral or show that it is divergent. tan-'x dx x² J1
Evaluate the integral or show that it is divergent. dx .2 4x? + 4x + 5 -00
Evaluate the integral or show that it is divergent. dx Г. — 2х -1 X
Evaluate the integral or show that it is divergent. х — 1 – dx Jo
Evaluate the integral or show that it is divergent. 1 dx 2 - 3x
Evaluate the integral or show that it is divergent. *4 In x х
Evaluate the integral or show that it is divergent. 9. dy Уу J2 Vy – 2
Evaluate the integral. 9x2 + 6x + 5
Evaluate the integral. /3 tan e de Sa/4 sin 20
Evaluate the integral. c1/2 Xe2r 2х dx хе (1 + 2х)2
Evaluate the integral. х dx х
Evaluate the integral. (cos x + sin x)² cos 2x dx
Evaluate the integral. tan 0 de 1 + tan 0
Evaluate the integral. dx Vx + x3/2
Evaluate the integral. (arcsin x)?dx
Evaluate the integral. -2 х dx 3/2 (4 — х?)92
Evaluate the integral. 'T/4 X sin x dx cosx 3.
Evaluate the integral. e*Ve* – 1 dx CIn 10 e* + 8
Evaluate the integral. dx e*/1 - e e-2x
Evaluate the integral. *3 dx |-3 1 + |x|
Evaluate the integral. Ух + 1 dx Ух - 1
Evaluate the integral. T/2 cos'x sin 2x dx ""
Evaluate the integral. x sin x cos x dx
Evaluate the integral. Зх3 Зx3 — х2 + 6х — 4 dx (x² + 1)(x² + 2)
Evaluate the integral. e cos x dxr
Evaluate the integral. dx XVx2 + 1
Evaluate the integral. Vī di cos
Evaluate the integral. dx Vx2 – 4x X,
Evaluate the integral. tan°0 sec'0 de tar
Evaluate the integral. + 8х — 3 .2 3 dx х3 + Зx2
Evaluate the integral. x cosh x dx
Evaluate the integral. sec°0 do tan²0
Evaluate the integral. х — 1 dx x? + 2х
Evaluate the integral. .2 + 2 dx x + 2
Evaluate the integral. dx х
Evaluate the integral. 2х e?x dx 1 + e 4x
Evaluate the integral. Vx? – 1 dx C2
Evaluate the integral. /arctan x dx .2 1 + x?
Evaluate the integral. sin(In t) dt
Evaluate the integral. dx le* – 1
Evaluate the integral. T/2 sir sin'0 cos?0 d0
Evaluate the integral. '2 Гx5 In x dx х dx
Evaluate the integral. dt 2t2 + 3t + 1
Evaluate the integral. *T/6 t sin 2t dt
Evaluate the integral. ,sinx dx sec x
Evaluate the integral. r2 ·dp. (x + 1)? J1
Evaluate the integral. (² (x + 1)² dx х
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example thatdisproves the statement.also diverges. If f(x) < g(x) and o g(x) dx
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.are both divergent, thenis divergent. If *
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f is a continuous, decreasing function on
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f is continuous on
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.(a) Every elementary function has an
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.The Midpoint Rule is always more accurate
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f is continuous, then f(x) dx = lim, - ,
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. z dx is convergent.
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. '4 dx = In 15 x? – 1
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. x? - 4 A - can be put in the form - + x(x²
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. x? + 4 A can be put in the form x? x*(x –
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. x? + 4 can be put in the form x(x? – 4) A
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. x(x² + 4) x? - 4 A can be put in the form x
Show that if a > -1 and b > a + 1, then the following integral is convergent. dx Jo 1 + xb
Find the value of the constant C for which the integralconverges. Evaluate the integral for this value of C. o, х dx Зх + 1 х + 1 .2
Show thatby interpreting the integrals as areas. Si e-*dx = {, /-In y dy
Show that So x'e* dx = } S%e*dx. 00
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
In a study of the spread of illicit drug use from an enthusiastic user to a population of N users, the authors model the number of expected new users by the equationwhere c, k and are positive
The average speed of molecules in an ideal gas iswhere M is the molecular weight of the gas, R is the gas constant, T is the gas temperature, and v is the molecular speed. Show that 3/2 4
Evaluateby the same method as in Exercise 55. dx x/x? – 4 o, -2 )2 х.
Sketch the region and find its area (if the area is finite). S = {(x, y) | x > 0, 0 < y< xe¯*}
Sketch the region and find its area (if the area is finite). S = {(x, y) | x> 1, 0 < y< 1/(x³ + x)}
Sketch the region and find its area (if the area is finite). S= {(x, y) | x < 0, 0 < y< e*}
Sketch the region and find its area (if the area is finite). S = {(x, y) | x> 1, 0 < y

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