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mathematics
precalculus
Calculus Of A Single Variable 11th Edition Ron Larson, Bruce H. Edwards - Solutions
Convert the polar equation to rectangular form and sketch its graph. 0 = 5л 6
Sketch a graph of the polar equation.r = 1/θ
Find all points (if any) of horizontal and vertical tangency to the curve on the given interval. x = 20 y = 2(1 cos 0) 0 ≤ 0 ≤ 2π 6 4 2 + -2 -2- - 2 4 6 8 10 12 14 X
Use a graphing utility to graph the polar equation. Find an interval for θ over which the graph is traced only once.r = -1 + sin θ
Find all points (if any) of horizontal and vertical tangency to the curve on the given interval. x = cos 0 + 0 sin 0 = sin cos 0 y = -2π ≤ ≤ 2π 8- 2 y -8-6 -2 -8+ H 468
Use a graphing utility to graph the polar equation. Find an interval for θ over which the graph is traced only once.r = 2 -5 cos θ
Find the arc length of the curve on the interval [0, 2π].Nephroid perimeter: x = a(3 cos t - cos 3t) y = a(3 sin t - sin 3t)
Use a graphing utility to graph the polar equation. Find an interval for θ over which the graph is traced only once.r = 4 + 3 cos θ
Find an equation of the tangent line to the curve at each given point. 2 3 x = 2 cot 8, y = 2 sinº 6, ( 5 ਹੈ), (0, 2), (2√3, -1)
Convert the polar equation to rectangular form and sketch its graph.r = 4
Convert the polar equation to rectangular form and sketch its graph.r = -6 csc θ
Convert the polar equation to rectangular form and sketch its graph.r = -1
Convert the rectangular equation to polar form and sketch its graph.y2 = 9x
Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results.x = t + 4, y = t3 - 12t + 6
The polar coordinates of a point are given. Plot the point and find the corresponding rectangular coordinates for the point. П 2
Convert the rectangular equation to polar form and sketch its graph.(x2 + y2)2 - 9 (x2 - y2) = 0
Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results.x = 9 - t, y = -t2
The rectangular coordinates of a point are given. Plot the point and find two sets of polar coordinates for the point for 0 = θ < 2π.(4, 5)
The polar coordinates of a point are given. Plot the point and find the corresponding rectangular coordinates for the point. -4, Зл 4
Convert the rectangular equation to polar form and sketch its graph.xy = 4
Plot the points below on the same set of coordinate axes. (r, 0) = (2,7) and (x, y) = (2,71)
The polar coordinates of a point are given. Plot the point and find the corresponding rectangular coordinates for the point. 7, 5 п 4
The rectangular coordinates of a point are given. Plot the point and find two sets of polar coordinates for the point for 0 = θ < 2π.(√7, -√7)
The rectangular coordinates of a point are given. Plot the point and find two sets of polar coordinates for the point for 0 = θ < 2π.(-5, -5√3)
The polar coordinates of a point are given. Plot the point and find the corresponding rectangular coordinates for the point. 0, Ιπ 6
The polar coordinates of a point are given. Plot the point and find the corresponding rectangular coordinates for the point. -2, 5л 3
The rectangular coordinates of a point are given. Plot the point and find two sets of polar coordinates for the point for 0 = θ < 2π.(-2√2, -2√2)
Find dy/dx and d2y/dx2, and find the slope and concavity (if possible) at the given value of the parameter. Parametric Equations x = 4t, y = 3t - 2 Parameter = 3 t
The rectangular coordinates of a point are given. Plot the point and find two sets of polar coordinates for the point for 0 = θ < 2π.(6, -2)
The polar coordinates of a point are given. Plot the point and find the corresponding rectangular coordinates for the point. -2, 11л 6
Under what circumstances can a graph that represents a set of parametric equations have more than one tangent line at a given point?
Explain how to write a polar equation in parametric form.
Find dy/dx.x = 3√t, y = 4 - t
Find dy/dx.x = sin2 θ, y = cos2 θ
The polar coordinates of a point are given. Plot the point and find the corresponding rectangular coordinates for the point.(√2, 2.36)
The polar coordinates of a point are given. Plot the point and find the corresponding rectangular coordinates for the point.(-8, 0.75)
The rectangular coordinates of a point are given. Plot the point and find two sets of polar coordinates for the point for 0 = θ < 2π.(1, 0)
The polar coordinates of a point are given. Plot the point and find the corresponding rectangular coordinates for the point.(-3, -1.57)
The polar coordinates of a point are given. Plot the point and find the corresponding rectangular coordinates for the point.(1.25, -5)
The rectangular coordinates of a point are given. Plot the point and find two sets of polar coordinates for the point for 0 = θ < 2π(0, -9)
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.The curve given by x = h + a cos θ and y = k + b sin θ has two horizontal asymptotes and two vertical asymptotes.
Consider the parametric equations(a) Use a graphing utility to graph the curve represented by the parametric equations.(b) Use a graphing utility to find the points of horizontal tangency to the curve.(c) Use the integration capabilities of a graphing utility to approximate the arc length of the
Find the area of the surface generated by revolving the curve about each given axis. x = ³, y = t + 1, 1 ≤ t ≤ 2, y-axis
Find the interval of convergence of the power series. 18 n=0 n!(x - 2)"
Consider the parametric equationsWhat is implied about the domain of the resulting rectangular equation? x = √√t-2 and y=+1, t≥ 2.
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 = t3, y = t2/2
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 = 4√t, y = 8 - t
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, y = e3t + 1
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 = e-t, y = e2t - 1
Use a graphing utility to graph the curve represented by the parametric equations (indicate the orientation of the curve). Eliminate the parameter and write the corresponding rectangular equation.x = cos3 θy = sin3 θ
Use a graphing utility to graph the curve represented by the parametric equations (indicate the orientation of the curve). Eliminate the parameter and write the corresponding rectangular equation.x = e-t, y = e3t
Use a graphing utility to graph the curve represented by the parametric equations (indicate the orientation of the curve). Eliminate the parameter and write the corresponding rectangular equation.x = e2t, y = et
Determine any differences between the curves of the parametric equations. Are the graphs the same? Are the orientations the same? Are the curves smooth? Explain.(a) x = t, y = t2(b) x = -t, y = t2
Eliminate the parameter and obtain the standard form of the rectangular equation.Line through (x1, y1) and (x2, y2):x = x1 + t(x2 - x1), y = y1 + t(y2 - y1)
To find a set of parametric equations for the line or conic.Line: passes through (-3, 1) and (1, 9)
To find a set of parametric equations for the line or conic.Circle: center: (-1/2, -4); radius: 1/2
To find a set of parametric equations for the line or conic.Ellipse: vertices: (-3, 0), (7, 0); foci: (-1, 0), (5, 0)
To find a set of parametric equations for the line or conic.Ellipse: vertices: (-1, 8), (-1, -12); foci: (-1, 4), (-1, -8)
To find a set of parametric equations for the line or conic.Hyperbola: vertices: (-2, 1), (0, 1); foci: (-3, 1), (1, 1)
Describe the orientation of the parametric equations x = t2 and y = t4 for -1 ≤ t ≤ 1.
Find the sequence of partial sums S1, S2, S3, S4, and S5. 3 + ا 3 + 1 + + +1+ 3 نیا 4 5 +
ConsiderWhat are the values of a and b in terms of n? f(x) = Σ 5x2m. n=0
Explain how to use a geometric power series to represent a function of the form f(x) b С CX
Determine the radius of convergence for the power seriesgiven the following result of the Ratio Test, where un = an(x - 2)n. 00 n=0 a,(x - 2)"
Match the sequence with the given nth term with its graph. [The graphs are labeled (a), (b), (c), and (d).] (a) an (c) 6 in 5 4 3 2 1 4 3 2 an -1+ 2 2 4 6 4 6 00 8 10 810 (b) (d) 6 4 2 -2 10 00 8 6 4 2 an an 2 4 2 8 10 4 6 8 10 n
Match the sequence with the given nth term with its graph. [The graphs are labeled (a), (b), (c), and (d).] (a) an (c) 6 in 5 4 3 2 1 4 3 2 an -1+ 2 2 4 6 4 6 00 8 10 810 (b) (d) 6 4 2 -2 10 00 8 6 4 2 an an 2 4 2 8 10 4 6 8 10 n
(a) Consider the power seriesin which the coefficients an = 1, 2, 3, 1, 2, 3, 1, . . . are periodic of period p = 3. Find the radius of convergence and the sum of this power series.(b) Consider a power seriesin which the coefficients are periodic, (an+p = ap), and an > 0. Find the radius of
What does the domain of represent? f(x) = Σ a (x = c)" - n=0
Match the sequence with the given nth term with its graph. [The graphs are labeled (a), (b), (c), and (d).]an = 10(0.3)n-1 (a) an (c) 6 in 5 4 3 2 1 4 3 2 an -1+ 2 2 4 6 4 6 00 8 10 810 (b) (d) 6 4 2 -2 10 00 8 6 4 2 an an 2 4 2 8 10 4 6 8 10 n
Explain how a Maclaurin polynomial and a power series centered at 0 for a function are different.
Find a power series for the function, centered at c, and determine the interval of convergence. f(x) = 1 6-x c=1
Write the first five terms of the sequence with the given nth term.an = 6n - 2
Use the definition of Taylor series to find the Taylor series, centered at c, for the function. 1 f(x) = 1 = ² x ² - c=2
The binomial series is used to represent a function of what form? What is the radius of convergence for the binomial series?
Find a power series for the function, centered at c, and determine the interval of convergence. f(x) = 2 6-x c = -2
Find a power series for the function, centered at c, and determine the interval of convergence. h(x) = 1 1 - 4x' c=0
Find a power series for the function, centered at c, and determine the interval of convergence. f(x) = 1 1 - 3x' c=0
Find the radius of convergence of the power series. 18 n=0 (3x)"
Use a graphing utility to graph the first 10 terms of the sequence with the given nth term. Use the graph to make an inference about the convergence or divergence of the sequence. Verify your inference analytically and, if the sequence converges, find its limit. an = cos nπ 3
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. a. 'n 1 n
Use the definition of Taylor series to find the Taylor series, centered at c, for the function.f(x) = e2x, c = 0
Use the definition of Taylor series to find the Taylor series, centered at c, for the function.f(x) = e-4x, c = 0
Use a graphing utility to graph f and its second-degree polynomial approximation P2 at x = c. Complete the table comparing the values of f and P2. 4 c = 1 √x' P₂(x) = 42(x - 1) + (x - 1)² 0 0.8 0.9 11.1 f(x) X = f(x) P₂(x) 1.2 2
Find a power series for the function, centered at c, and determine the interval of convergence. g(x) || 5 2x - 3' c = -3
Find the radius of convergence of the power series. 18 n=1 (4x)n n²
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. I + zu n || an
Find the radius of convergence of the power series. 18 n=0 (-1) xn 5n
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an = UIN Л +5
Find a power series for the function, centered at c, and determine the interval of convergence. f(x) 2 50+4 c = -1
Find the radius of convergence of the power series. 18 n=0 x²n (2n)!
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an 2n3 - 1 3n + 4
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. a n || (4n)! (4n 1)!
Find a power series for the function, centered at c, and determine the interval of convergence. f(x) 4 3x + 2' c=3
Find the radius of convergence of the power series. 18 n=0 (2n)!x³n n n!
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. n || ܐ e In n
Imagine you are stacking an infinite number of spheres of decreasing radii on top of each other, as shown in the figure. The radii of the spheres are 1 meter, 1/√2 meter, 1/√3 meter, and so on. The spheres are made of a material that weighs 1 newton per cubic meter.(a) How high is this infinite
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an = sin √n n
Use the power seriesto find a power series for the function, centered at 0, and determine the interval of convergence. 1 1 + x = Σ (−1)"x", |x|
Use the power seriesto find a power series for the function, centered at 0, and determine the interval of convergence. 1 1 + x = Σ (−1)"x", |x|
Determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an n In n
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