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mathematics
calculus 10th edition

Questions and Answers of Calculus 10th Edition

In Exercises sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.x = et -
In Exercises find a polar equation for the conic with its focus at the pole. (For convenience, the equation for the directrix is given in rectangular form.) Conic Parabola Eccentricity e =
In Exercises sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.x = e4t, y
In Exercises find a polar equation for the conic with its focus at the pole. (For convenience, the equation for the directrix is given in rectangular form.) Conic Ellipse Eccentricity e =
In Exercises find a polar equation for the conic with its focus at the pole. (For convenience, the equation for the directrix is given in rectangular form.) Conic Parabola Eccentricity e =
In Exercises sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.x = 6 cos
In Exercises find a polar equation for the conic with its focus at the pole. (For convenience, the equation for the directrix is given in rectangular form.) Conic Ellipse Eccentricity e Directrix y =
In Exercises sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.x = 2 + 5
The rotary engine was developed by Felix Wankel in the 1950s. It features a rotor that is a modified equilateral triangle. The rotor moves in a chamber that, in two dimensions, is an epitrochoid. Use
In Exercises sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter. x =
In Exercises find a polar equation for the conic with its focus at the pole. (For convenience, the equation for the directrix is given in rectangular form.) Conic Hyperbola Eccentricity e =
In Exercises find a polar equation for the conic with its focus at the pole. (For convenience, the equation for the directrix is given in rectangular form.) Conic Hyperbola Eccentricity e =
In Exercises sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.x = 5
In Exercises find a polar equation for the conic with its focus at the pole. (For convenience, the equation for the directrix is given in rectangular form.) Conic Parabola Vertex or
In Exercises find dy/dx and d²y/dx², and find the slope and concavity (if possible) at the given value of the parameter. Parametric x = t - 6, y = 1² Equations Parameter t = 5
In Exercises find two different sets of parametric equations for the rectangular equation.y = 4x + 3
In Exercises find dy/dx and d²y/dx², and find the slope and concavity (if possible) at the given value of the parameter. Parametric Equations x = 2 + 5t, y = 1 - 4t Parameter t = 3
In Exercises find dy/dx and d²y/dx², and find the slope and concavity (if possible) at the given value of the parameter. Parametric Equations x = -1/-² y = 2t + 3 t' Parameter t = -1
In Exercises find two different sets of parametric equations for the rectangular equation.y = x² - 2
In Exercises find dy/dx and d²y/dx², and find the slope and concavity (if possible) at the given value of the parameter. Parametric Equations
In Exercises find a polar equation for the conic with its focus at the pole. (For convenience, the equation for the directrix is given in rectangular form.) Conic Parabola Vertex or Vertices (5, TT)
In Exercises find a polar equation for the conic with its focus at the pole. (For convenience, the equation for the directrix is given in rectangular form.) Conic Hyperbola Vertex or
In Exercises find a polar equation for the conic with its focus at the pole. (For convenience, the equation for the directrix is given in rectangular form.) Conic Ellipse Vertex or Vertices (2, 0),
In Exercises find a polar equation for the conic with its focus at the pole. (For convenience, the equation for the directrix is given in rectangular form.) Conic Ellipse Vertex or
In Exercises find dy/dx and d²y/dx², and find the slope and concavity (if possible) at the given value of the parameter. Parametric Equations x = 5 + cos 0, y = 3 + 4 sin Parameter TT 6 0 =
In Exercises find dy/dx and d²y/dx², and find the slope and concavity (if possible) at the given value of the parameter. Parametric Equations x = cos³ 0, y = 4 sin³ 0 Parameter TT 3 Ꮎ
In Exercises find dy/dx and d²y/dx², and find the slope and concavity (if possible) at the given value of the parameter. Parametric Equations x = 10 cos 0, y = 10 sin 0 Parameter 0 TT 4
In Exercises find a polar equation for the conic with its focus at the pole. (For convenience, the equation for the directrix is given in rectangular form.) Conic Hyperbola Vertex or Vertices (2, 0),
In Exercises(a) Use a graphing utility to graph the curve represented by the parametric equations, (b) Use a graphing utility to find dx/dθ, dy/dθ, and dy/dx at the given value of the
In Exercises find dy/dx and d²y/dx², and find the slope and concavity (if possible) at the given value of the parameter. Parametric Equations x = e¹, y = et Parameter t = 1
Identify each conic.(a)(b)(c)(d) || 5 1 - 2 cos 0
In Exercises(a) Use a graphing utility to graph the curve representedby the parametric equations, (b) Use a graphing utility to find dx/dθ, dy/dθ, and dy/dx at the given value of the
Find a polar equation for the ellipse with focus (0, 0), eccentricity 1/2, and a directrix at r = 4 sec θ.
Identify the conic in the graph and give the possible values for the eccentricity.(a)(b)(c)(d) 元2+ + 0 1/2
Find a polar equation for the hyperbola with focus (0, 0), eccentricity 2, and a directrix at r = -8 csc θ.
Show that the polar equation forisEllipse. X x2 a2 y2 6²
Show that the polar equation forisHyperbola. a² b² = 1
In Exercises find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results.x = 5 - t, y = 2t²
Describe what happens to the distance between the directrix and the center of an ellipse when the foci remain fixed and e approaches 0.
In Exercises find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results.x = t + 2, y = t³ - 2t
In Exercises find the arc length of the curve on the given interval. Parametric Equations x = ²² + 1, y = 41³ + 3 Interval 0 ≤t≤2
In Exercises find the area of the surface generated by revolving the curve about (a) The x-axis(b) The y-axis x = 1, y = 3t, 0≤ t ≤ 2
In Exercises find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results.x = 2 + 2 sin θ, y = 1 + cos θ
In Exercises find the arc length of the curve on the given interval. Parametric Equations x = 6 cos 0, y = 6 sin Interval 0 ≤ 0 ≤ T
In Exercises use the results to write the polar form of the equation of the conic. x² 9 y² 16 1
In Exercises find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results.x = 2 - 2 cos θ, y = 2 sin 2θ
In Exercises use the results to write the polar form of the equation of the conic. x² 4 + y² = 1
In Exercises use the integration capabilities of a graphing utility to approximate, to two decimal places, the area of the region bounded by the graph of the polar equation. r = 3 2 cos 0
In Exercises find the area of the surface generated by revolving the curve about (a) The x-axis(b) The y-axis x = 2 cos 0, y = 2 sin 0, 0≤ 0 ≤ 2
In Exercises use the results to write the polar form of the equation of the conic.Ellipse: focus at (4, 0); vertices at (5, 0), (5, π)
In Exercises find the area of the region. x = 2 cos 0 y sin 0 0 ≤ 0 ≤ T -3-2 3 برا 2 y -2 -3+ 12 3 X
In Exercises use the integration capabilities of a graphing utility to approximate, to two decimal places, the area of the region bounded by the graph of the polar equation. r = 9 4 + cos 0
In Exercises find the area of the region. x = 3 sin 0 y = 2 cos 0 ㅠ ≤0≤ 4 نرا 3 1 -3-2 ¹1 y 2 -2+ 12 3 X
In Exercises use the results to write the polar form of the equation of the conic.Hyperbola: focus at (5, 0); vertices at (4, 0), (4, π)
In Exercises plot the point in polar coordinates and find the corresponding rectangular coordinates of the point. -6, 7 п 6
In Exercises use the integration capabilities of a graphing utility to approximate, to two decimal places, the area of the region bounded by the graph of the polar equation. 3 6 + 5 sin 0
In Exercises plot the point in polar coordinates and find the corresponding rectangular coordinates of the point. 5, З п 2
In Exercises use the integration capabilities of a graphing utility to approximate, to two decimal places, the area of the region bounded by the graph of the polar equation. 2 3 - 2 sin 0
On November 27, 1963, the United States launched Explorer 18. Its low and high points above the surface of Earth were approximately 119 miles and 123,000 miles (see figure). The center of Earth is a
In Exercises plot the point in polar coordinates and find the corresponding rectangular coordinates of the point. (√3, 1.56)
The planets travel in elliptical orbits with the sun as a focus, as shown in the figure.(a) Show that the polar equation of the orbit is given by(b) Show that the minimum distance (perihelion) from
In Exercises use Exercise 62 to find the polar equation of the elliptical orbit of the planet, and the perihelion and aphelion distances.Data from in Exercise 62The planets travel in elliptical
In Exercises plot the point in polar coordinates and find the corresponding rectangular coordinates of the point.(-2, -2.45)
In Exercises the rectangular coordinates of a point are given. Plot the point and find two sets of polar coordinates of the point for 0 ≤ θ < 2π.(4, -4)
In Exercises use Exercise 62 to find the polar equation of the elliptical orbit of the planet, and the perihelion and aphelion distances.Data from in Exercise 62The planets travel in elliptical
In Exercises use Exercise 62 to find the polar equation of the elliptical orbit of the planet, and the perihelion and aphelion distances.Data from in Exercise 62The planets travel in elliptical
In Exercises use Exercise 62 to find the polar equation of the elliptical orbit of the planet, and the perihelion and aphelion distances.Data from in Exercise 62The planets travel in elliptical
In Exercises the rectangular coordinates of a point are given. Plot the point and find two sets of polar coordinates of the point for 0 ≤ θ < 2π. (-√3,-√3)
In Exercises let r0 represent the distance from a focus to the nearest vertex, and let r₁ represent the distance from the focus to the farthest vertex.Show that the eccentricity of an ellipse can
In Exercises the rectangular coordinates of a point are given. Plot the point and find two sets of polar coordinates of the point for 0 ≤ θ < 2π.(0, -7)
In Exercises the rectangular coordinates of a point are given. Plot the point and find two sets of polar coordinates of the point for 0 ≤ θ < 2π.(-1, 3)
In Exercises let r0 represent the distance from a focus to the nearest vertex, and let r₁ represent the distance from the focus to the farthest vertex.Show that the eccentricity of a hyperbola can
In Exercises convert the rectangular equation to polar form and sketch its graph.x² + y² = 25
In Exercises convert the rectangular equation to polar form and sketch its graph.x² - y² = 4
In Exercises convert the rectangular equation to polar form and sketch its graph.y = 9
In Exercises convert the rectangular equation to polar form and sketch its graph.x = 6
In Exercises use a graphing utility to graph the polar equation. 3 cos(0 - π/4)
In Exercises convert the rectangular equation to polar form and sketch its graph.x² = 4y
In Exercises convert the rectangular equation to polar form and sketch its graph.x² + y² - 4x = 0
In Exercises convert the polar equation to rectangular form and sketch its graph.r = 3 cos θ
In Exercises convert the polar equation to rectangular form and sketch its graph. 0 = З п 4
In Exercises convert the polar equation to rectangular form and sketch its graph.r = 10
In Exercises convert the polar equation to rectangular form and sketch its graph.r = 6 sin θ
In Exercises convert the polar equation to rectangular form and sketch its graph.r = 3 csc θ
In Exercises convert the polar equation to rectangular form and sketch its graph.r = -2 sec θ tan θ
In Exercises use a graphing utility to graph the polar equation.r = 2 sin θ cos² θ
In Exercises use a graphing utility to graph the polar equation.r = 4 cos 2θ sec θ
In Exercises sketch a graph of the polar equation. 0 = TT 10
In Exercises use a graphing utility to graph the polar equation.r = 4 (sec θ - cos θ)
In Exercises find the points of horizontal and vertical tangency (if any) to the polar curve.r = 1 - cos θ
In Exercises find the points of horizontal and vertical tangency (if any) to the polar curve.r = 3 tan θ
In Exercises sketch a graph of the polar equation and find the tangents at the pole.r = 4 sin 3θ
In Exercises sketch a graph of the polar equation and find the tangents at the pole.r = 3 cos 4θ
In Exercises sketch a graph of the polar equation.r = 6
In Exercises sketch a graph of the polar equation.r = - sec θ
In Exercises sketch a graph of the polar equation.r = 5 csc θ
In Exercises sketch a graph of the polar equation.r² = 4 sin² 2θ
In Exercises sketch a graph of the polar equation.r = 3 - 4 cos θ
In Exercises sketch a graph of the polar equation.r = 4 - 3 cos θ
In Exercises sketch a graph of the polar equation.r = 4θ

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