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mathematics
calculus early transcendentals 9th

Questions and Answers of Calculus Early Transcendentals 9th

(a) Show thatcos(x2) ≥ cos x for 0 ≤ x ≤ 1.(b) Deduce that 9/1 cos(x²) dx = 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.The center of mass of a lamina of uniform
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 probability density function, then
Find the area of the surface obtained by rotating the curve in Exercise 9 about the y-axis.Data From Exercise 9:Find the length of the curve y = √√√t - 1 dt 1 ≤ x ≤ 16
Find the solution of the differential equation that satisfies the given initial condition. x + 3y²√√x² + 1 dy dx = 0, y(0) = 1
A Bernoulli differential equation (named after James Bernoulli) is of the formSolve the differential equation xy' + y = –xy2. dy dx + P(x)y = Q(x)y"
(a) Solve the differential equation(b) Solve the initial-value problemy(0) = 0, and graph the solution.(c) Does the initial-value problemy(0) = 2, have a solution? Explain. y' = 2x√/1 - y².
We considered a 95°C cup of coffee in a 20°C room. Suppose it is known that the coffee cools at a rate of 1°C per minute when its temperature is 70°C.(a) What does the differential equation
Find the vertex, focus, and directrix of the parabola and sketch its graph.x2 = 8y
Find dx/dt, dy/dt, and dy/dx.x = 2t3 + 3t, y = 4t − 5t2
Find the area of the region that is bounded by the given curve and lies in the specified sector.r = √2θ, 0 ≤ θ ≤ π/2
Write a polar equation of a conic with the focus at the origin and the given data.Parabola, directrix x = 2
Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with r > 0 and one with r < 0.(a) (1, π/4)(b) (−2, 3π/2)(c) (3, −π/3)
For the given parametric equations, find the points (x, y) corresponding to the parameter values t = −2, −1, 0, 1, 2.x = t2 + t, y = 3t+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.If the parametric curve x = f(t), y = g(t)
Sketch the parametric curve and eliminate the parameter to find a Cartesian equation of the curve.x = t2 + 4t, y = 2 – t, –4 ≤ t ≤ 1
Find the vertex, focus, and directrix of the parabola and sketch its graph.9x = y2
Find the area of the region that is bounded by the given curve and lies in the specified sector.r = eθ, 3π/4 ≤ θ ≤ 3π/2
Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with r > 0 and one with r < 0.(a) (2, 5π/6)(b) (1, −2π/3)(c) (−1, 5π/4)
For the given parametric equations, find the points (x, y) corresponding to the parameter values t = − 2, −1, 0, 1, 2.x = ln(t2 + 1), y = t/(t + 4)
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 x = f(t) and y = g(t) are twice
Sketch the parametric curve and eliminate the parameter to find a Cartesian equation of the curve.x = 1 + e2t, y = et
Find the vertex, focus, and directrix of the parabola and sketch its graph.5x + 3y2 = 0
Plot the point whose polar coordinates are given. Then find the Cartesian coordinates of the point.(a) (2, 3π/2)(b) (√2, π/4)(c) (−1, 2π/6)
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 length of the curve x = f(t), y = g(t), a
Find the vertex, focus, and directrix of the parabola and sketch its graph.x2 + 12y = 0
Sketch the parametric curve and eliminate the parameter to find a Cartesian equation of the curve.x = ln t, y = t2
Find dx/dt, dy/dt, and dy/dx.x = t + sin(t2 + 2), y = tan(t2 + 2)
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 the position of a particle at time t is
Sketch the parametric curve and eliminate the parameter to find a Cartesian equation of the curve.x = 2 cos θ, y = 1 + sin θ
Find the vertex, focus, and directrix of the parabola and sketch its graph(y + 1)2 = 16(x – 3)
Find the slope of the tangent to the parametric curve at the indicated point.x = t2 + 2t, y = 2t − 2t УА 0 (15,2) X
Show that any tangent line to a hyperbola touches the hyperbola halfway between the points of intersection of the tangent and the asymptotes.
Write a polar equation of a conic with the focus at the origin and the given data.Ellipse, eccentricity 2/3, vertex (2, π)
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 a point is represented by (x, y) in
A circle C of radius 2r has its center at the origin. A circle of radius r rolls without slipping in the counterclockwise direction around C. A point P is located on a fixed radius of the rolling
Find the vertex, focus, and directrix of the parabola and sketch its graph.(x – 3)2 = 8(y + 1)
Find the slope of the tangent to the parametric curve at the indicated point.x = t + cos πt, y = −t + sin πt У X (3,-2)
Write a polar equation of a conic with the focus at the origin and the given data.Ellipse, eccentricity 0.6, directrix r = 4 csc θ
Evaluate the definite integral. Jo cos(πt/2) dt
Ifandfind Sof(x) dx = 37
The boundaries of the shaded region are the y-axis, the line y = 1, and the curveFind the area of this region by writing x as a function of y and integrating with respect to y (as in Exercise
Sketch the region enclosed by the given curves and calculate its area.y = 2x – x2, y = 0
Ifandfind f f(x) dx = 7.3
Evaluate the indefinite integral. [x³√x² + 1 dx
Use Property 8 of integrals to estimate the value of the integral. 1 3 J2 √₂ x² + 2 dx
Find the derivative of the function. -√3x+ sin(1¹) dt J2x y= = 2
The area of the region that lies to the right of the y-axis and to the left of the parabola x = 2y – y2 (the shaded region in the figure) is given by the integral ∫20 (2y – y2) dy. (Turn
Find the derivative of the function. y= y = S/² - انة - dt
Evaluate the integral. f(x) dx where f(x)= = 2 4x² if -2≤x≤0 if 0 < x≤ 2
Find the derivative of the function. g(x) - Sinx 17/4 1-1² + dt
Repeat Exercise 55 for the curve y = (x2 + 1)–1 – x4.Data From Exercise 55:Use a graph to estimate the x-intercepts of the curve y = 1 – 2x – 5x4. Then use this information to estimate the
Evaluate the definite integral. *3π/2 3*/² | sin x | dx Jo
Find the derivative of the function. g(x) = f*cos(1²) dt
Evaluate the integral. f(x) dx where f(x). = [sin x cos x if 0
Evaluate the definite integral. ²₁ (x-2x) dx
Evaluate the indefinite integral. fx(2x + 5)³ dx
Evaluate the integral. 1/√2 4 √1/2 √1-x² dx
Find the derivative of the function. F(x)=√t + sint dt
Evaluate the indefinite integral. f x² √2 + x dx
Evaluate the definite integral. Jo |2x - 1| dx
Find the derivative of the function. 1² Jo 1 + 1³ F(x) = fr dt
Evaluate the integral. 4 Jo 2³ 2³ ds
Evaluate the definite integral. Jo 31² - 1 2 - dt 4 tf- 1
Evaluate the integral. 3 (3x + 1)² - dx S²- X 3
Evaluate the indefinite integral. 1 + x 1 + x² dx
The regions A, B, and C bounded by the graph of f and the x-axis have areas 3, 2, and 1, respectively. Evaluate the integral.a.b. y 0 A f В C X
Evaluate the indefinite integral. X 1 + x4 dx
Evaluate the definite integral. #/2 Jπ/6 csc t cot t dt
The regions A, B, and C bounded by the graph of f and the x-axis have areas 3, 2, and 1, respectively. Evaluate the integral.a.b. y 0 A f В C X
Evaluate the integral. √√3 SYNST -dx 8 J₁/√/3 1 + x²
Evaluate the definite integral. √√3/2 Jo dr √1 r² -
Evaluate the indefinite integral. dx /1-x² sin ¹x
Evaluate the integral. Jo cosh t dt
Evaluate the integral. f'(x² + e²) dx
Evaluate the definite integral. 10 2e* -10 sinh x + cosh x - dx
Find the area under the graph of y = sin x and above the x-axis, between x = 0 and x = π/2.
Evaluate the indefinite integral. cos(In t) t at
Evaluate the definite integral. 4 3 3 X - dx
Evaluate the indefinite integral. f cotx dx
Find the area under the graph of y = x2 + 5 and above the x-axis, between x = 0 and x = 4.
Evaluate the integral. 18 3 SH √ √ E JI Z dz
Evaluate the definite integral. Jo /3 sin+sin 0 tan²0 sec ²0 de
Evaluate the indefinite integral. sin x 1 + cos²x -dx
Evaluate the integral. v³ + 3vº 04 $².0³. dv
Evaluate the integral by interpreting it in terms of areas. -4 2 (2x - √16 - x²) dx
Evaluate the indefinite integral. sin 2x 1 + cos²x dx
Evaluate the integral. (2 sin x - e¹) dx
Evaluate the definite integral. =/4 1 + cos²0 Jo cos²0 - de
Evaluate the definite integral. *T/4 √5/4 (3e+ (3e - 4 sec x tan x) dx Jo
Evaluate the indefinite integral. dt cos²t√1 + tan t
Evaluate the integral. f'(1 + r)³ dr
Evaluate the definite integral. -2 (sinh x + cosh x) dx
Evaluate the indefinite integral. sinh²x cosh x dx
Evaluate the definite integral. f (5x - 5³) dx Jo
Evaluate the integral, if it exists. S₁ | √x – 1 | dx
Evaluate the indefinite integral. 2¹ J2¹ +3 - dt
Evaluate the integral. 3 y³ - 2y²-y dy y² 2
Evaluate the integral by interpreting it in terms of areas. 3 ³₁ (2x - 1) dx -1
Evaluate the integral, if it exists. ²1x² - 4|dx

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