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mathematics
precalculus

Calculus Of A Single Variable 11th Edition Ron Larson, Bruce H. Edwards - Solutions

Find a power series for the function, centered at c, and determine the interval of convergence. f(x) = 5 4-x² c=0
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|
Find the interval of convergence of the power series. n=0 (-1)" xn (n + 1)(n + 2)
Find the nth Maclaurin polynomial for the function.f(x) = xex, n = 4
Find the nth Maclaurin polynomial for the function.f(x) = x2e-x, n = 4
Find the interval of convergence of the power series. 18 (-1)^+1x 6
Find the nth Maclaurin polynomial for the function. f(x) 1 1 - x' n = 5
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|
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|
Find the interval of convergence of the power series. n=0 (x - 3) +1 (n + 1)4"+1
Find the interval of convergence of the power series. n=0 (-1)" n!(x - 5) 3″
Find the interval of convergence of the power series. n=1 (-1)+¹(x-4)" n9"
Find the interval of convergence of the power series. Ё n=0 (-1)"+(x - 1)"+1 n+1
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.f(x) = ln(x2 + 1) 1 1 + x = Σ (−1)"x", |x|
Find the Maclaurin series for the function. Use the table of power series for elementary functions shown below.g(x) = e-x/3 POWER SERIES FOR ELEMENTARY FUNCTIONS Function X 1 (x-1) + (x - 1)²(x - 1)³ + (x - 1)4+ (-1)^(x − 1)² + ··· - 1 + x = 1x + ²x³ + x²-1³ +.. - - In x = (x - 1) et =
Find the sequence of partial sums S1, S2, S3, S4, and S5. −7+1-17 + 1 49 1 343
Find the interval of convergence of the power series. 18 n=1 (x-3)2-1 3n-1
Find the interval of convergence of the power series. 18 n=0 (-1)"x²n+1 2n + 1
Find the interval of convergence of the power series. n=1 (-1)^+¹(x-2)^ n2n
Find the sum of the convergent series. 18 n=0 2l5 FL
Find the interval of convergence of the power series. n=1 n n+ 1 (-2x)"-1
(a) Use a graphing utility to graph several partial sums of the series(b) Find the sum of the series and its radius of convergence,(c) Use a graphing utility and 50 terms of the series to approximate the sum when x = 0.5,(d) Determine what the approximation represents and how good the approximation
Use the power seriesto find a power series for the function, centered at 0, and determine the interval of convergence.f(x) = arctan 2x 1 1 + x = Σ (−1)"x", |x|
Find the sum of the convergent series. 18 n=0 3n+2 In
Find the sum of the convergent series. 00 Σ [(0.4) + (0.9)"] n=0
(a) Use the Maclaurin polynomials P1(x), P3(x), and P5(x) for f(x) = sin x to complete the table.(b) Use a graphing utility to graph f(x) = sin x and the Maclaurin polynomials in part (a).(c) Describe the change in accuracy of a polynomial approximation as the distance from the point where the
Find the interval of convergence of the power series. 18 n=0 3n+1 X (3n + 1)!
Find the Maclaurin series for the function. Use the table of power series for elementary functions shown below.f(x) = arcsin πx POWER SERIES FOR ELEMENTARY FUNCTIONS Function X 1 (x-1) + (x - 1)²(x - 1)³ + (x - 1)4+ (-1)^(x − 1)² + ··· - 1 + x = 1x + ²x³ + x²-1³ +.. - - In x = (x -
Find the interval of convergence of the power series. 18 n=0 (-1) x²n n!
Find the Maclaurin series for the function. Use the table of power series for elementary functions shown below.g(x) = arctan 5x POWER SERIES FOR ELEMENTARY FUNCTIONS Function X 1 (x-1) + (x - 1)²(x - 1)³ + (x - 1)4+ (-1)^(x − 1)² + ··· - 1 + x = 1x + ²x³ + x²-1³ +.. - - In x = (x -
Find the sum of the convergent series. Σ[(3) n=0 1 (n + 1)(n + 2)]
Find the interval of convergence of the power series. 18 n=1 n!x" (2n)!
(a) Use the Taylor polynomials P1(x), P2(x), and P4(x) for f(x) = ex, centered at c = 1, to complete the table.(b) Use a graphing utility to graph f(x) = ex and the Taylor polynomials in part (a).(c) Describe the change in accuracy of polynomial approximations as the degree increases.
Use the power seriesto find a power series for the function, centered at 0, and determine the interval of convergence. 1 1-x ܐ Σx", x < 1
Find the interval of convergence of the power series. Σ και 2.4.6.2n 5.7 (2n + 1)] x2n+1
Find the interval of convergence of the power series. n=1 2.3.4 (n + 1)x" · n!
Find the interval of convergence of the power series. n=1 . - (−1)+¹3•7•11· · · (4n − 1)(x − 3)″ 4n
(a) Write the repeating decimal as a geometric series and(b) Write the sum of the series as the ratio of two integers.0.09̅
Use a geometric series or the nth-Term Test to determine the convergence or divergence of the series. Σ 9-" n=0
(a) Write the repeating decimal as a geometric series and(b) Write the sum of the series as the ratio of two integers.0.64̅
Use the Direct Comparison Test or the Limit Comparison Test to determine the convergence or divergence of the series. 18 n=0 7n 8" + 5
Use the power seriesto find a power series for the function, centered at 0, and determine the interval of convergence. 1 1-x ܐ Σx", x < 1
Find the interval of convergence of the power series. n=1 n!(x + 1)n (2n-1) 1.3.5
Find the Maclaurin series for the function. Use the table of power series for elementary functions shown below:f(x) = cos2 x POWER SERIES FOR ELEMENTARY FUNCTIONS Function X 1 (x-1) + (x - 1)²(x - 1)³ + (x - 1)4+ (-1)^(x − 1)² + ··· - 1 + x = 1x + ²x³ + x²-1³ +.. - - In x = (x - 1) et =
Find the interval of convergence of the power series, where c > 0 and k is a positive integer. 18 n=0 X n
Find the interval of convergence of the power series, where c > 0 and k is a positive integer. n=1 (-1)"+¹(x-c)" nch
Use a geometric series or the nth-Term Test to determine the convergence or divergence of the series. 18 n=1 5n! + 6 n! + 1
Find the interval of convergence of the power series, where c > 0 and k is a positive integer. n=1 k(k+ 1)(k + 2) (k+ n − 1)x" n! .
Find the sum of the convergent series by using a well-known function. Identify the function and explain how you obtained the sum. 2n Σ (-1)+1. 5"n n=1
Find the interval of convergence of the power series, where c > 0 and k is a positive integer. 8 n=1 n!(x - c)" 1.3.5 . (2n (2n-1)
Write an equivalent series with the index of summation beginning at n = 1. 18 n= IP X² (7n - 1)!
Write an equivalent series with the index of summation beginning at n = 1. 18 n=2 3n-1 (2n - 1)!
A manufacturer producing a new product estimates the annual sales to be 9600 units. Each year, 8% of the units that have been sold will become inoperative. So, 9600 units will be in use after 1 year, [9600 + 0.92(9600)] units will be in use after 2 years, and so on. How many units will be in use
Find the sum of the convergent series by using a well-known function. Identify the function and explain how you obtained the sum. 1 22n+1(2n + 1) 00 Σ (−1)", n=0
Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001. f(x) 1 x - 2' approximate f(0.15)
Find the Maclaurin series for the function.f(x) = x sin x
The figure on the left shows the graph of a function. The figure on the right shows the graph of a power series representation of the function.(a) Identify the function.(b) What are the center and interval of convergence of the power series? 6 (0,5) 4 2 -2 -2 2 4 6 x 5(0,5) 14 3 2 1 2 3 4 5 X
Find the Maclaurin series for the function.h(x) = x cos x
Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001. f(x) = 1 x + l' approximate f(0.2)
Letand(a) Find the intervals of convergence of f and g.(b) Show that f'(x) = g(x) and g'(x) = -f(x).(c) Identify the functions f and g. (-1)^x2n+1 (2n + 1)! f(x) = ₁ n=0
Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001.f(x) = sin x, approximate f(0.3)
Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001.f(x) = cos x, approximate f(0.4)
Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001.f(x) = ex, approximate f(0.6)
Write a power series that has the indicated interval of convergence. Explain your reasoning.[-3, 7]
Use a graphing utility to show that √8 (4n)!(1103 +26,390n) 9801 (n!)3964n n=0 1 П
Determine the degree of the Maclaurin polynomial required for the error in the approximation of the function at the indicated value of x to be less than 0.001.f(x) = ln(x + 1), approximate f(1.25)
Let and(a) Find the intervals of convergence of f and g.(b) Show that f'(x) = g(x) and g'(x) = f(x).(c) Identify the functions f and g. 2n+1 (2n + 1)! f(x) = 2₁ n=0
The figure shows the graphs of the first-, second-, and third-degree polynomial approximations P1, P2, and P3 of a function f. Label the graphs of P1, P2, and P3. To print an enlarged copy of the graph, go to MathGraphs.com. t -20 10 8 642 -2 -4+ 10 20
Use Theorem 9.15 to determine the number of terms required to approximate the sum of the series with an error of less than 0.0001. THEOREM 9.15 Alternating Series Remainder If a convergent alternating series satisfies the condition a,+1 a,, then the absolute value of the remainder R, involved in
Use Theorem 9.15 to determine the number of terms required to approximate the sum of the series with an error of less than 0.0001. THEOREM 9.15 Alternating Series Remainder If a convergent alternating series satisfies the condition a,+1 a,, then the absolute value of the remainder R, involved in
Use the Alternating Series Test, if applicable, to determine the convergence or divergence of the series. n=1 (-1)"+1 √√n 4√/n + 2
What is the relationship between the equation of a tangent line to a differentiable function at a point and the first Taylor polynomial for that function centered at the point?
The Bessel function of order 1 is(a) Show that the series converges for all x.(b) Show that the series is a solution of the differential equation (c) Use a graphing utility to graph the polynomial composed of the first four terms of J1.(d) Use J0 from Exercise 65 to show that J0'(x) = -J1(x).Use
The Bessel function of order 0 is(a) Show that the series converges for all x.(b) Show that the series is a solution of the differential equation (c) Use a graphing utility to graph the polynomial composed of the first four terms of J0.(d) Approximate ∫10 J0 dx accurate to two decimal places.
Use the Ratio Test or the Root Test to determine the convergence or divergence of the series. M8 n=1 4n 7n 1, 71
Use the Ratio Test or the Root Test to determine the convergence or divergence of the series. 18 n=0 7n (2n + 3)"
(a) Compare the Maclaurin polynomials of degree 4 and degree 5, respectively, for the functions f(x) = ex and g(x) = xex. What is the relationship between them?(b) Use the result in part (a) and the Maclaurin polynomial of degree 5 for f (x) = sin x to find a Maclaurin polynomial of degree 6 for
Use the Ratio Test or the Root Test to determine the convergence or divergence of the series. 18 n en² n=1
(a) Differentiate the Maclaurin polynomial of degree 5 for f(x) = sin x and compare the result with the Maclaurin polynomial of degree 4 for g(x) = cos x.(b) Differentiate the Maclaurin polynomial of degree 6 for f(x) = cos x and compare the result with the Maclaurin polynomial of degree 5 for g(x)
Find a geometric power series for the function, centered at 0. h(x) 3 2+x
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.The eccentricity of a hyperbola with a horizontal transverse axis is e = √1 + m2, where m and -m the slopes of the asymptotes.
Find equations for (a) The tangent lines(b) The normal lines to the hyperbola for the given value of x. (The normal line at a point is perpendicular to the tangent line at the point.) y2 4 | 2 = 1, x = 4
A hyperbolic mirror (used in some telescopes) has the property that a light ray directed at the focus will be reflected to the other focus. The mirror in the figure has the equationAt which point on the mirror will light from the point (0, 10) be reflected to the other focus? क 36 y2 64 = 1.
Find equations for (a) The tangent lines(b) The normal lines to the hyperbola for the given value of x. (The normal line at a point is perpendicular to the tangent line at the point.) 9 = x 'I = z[ - 9 ल
On January 31, 1958, the United States launched the research satellite Explorer 1. Its low and high points above the surface of Earth were 220 miles and 1563 miles. Find the eccentricity of its elliptical orbit. (Use 4000 miles as the radius of Earth.)
Consider the equation 9x2 + 4y2 - 36x - 24y - 36 = 0.(a) Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola.(b) Change the 4y2-term in the equation to -4y2. Classify the graph of the new equation.(c) Change the 9x2-term in the original equation to 4x2. Classify
Find the center, foci, vertices, and eccentricity of the hyperbola, and sketch its graph using asymptotes as an aid. (y + 3)² (x - 5)² 225 64 = 1
Find the standard form of the equation of the hyperbola with the given characteristics.Vertices: (0, 2), (6, 2)Asymptotes: y = 2/3xy = 4 - 2/3x
Find the standard form of the equation of the hyperbola with the given characteristics.Center: (0, 0)Vertex: (6, 0)Focus: (10, 0)
Find the standard form of the equation of the hyperbola with the given characteristics.Center: (0, 0)Vertex: (0, 2)Focus: (0, 4)
Find the standard form of the equation of the hyperbola with the given characteristics.Vertices: (2, ±3)Foci: (2, ±5)
Find the standard form of the equation of the hyperbola with the given characteristics.Vertices: (2, ±3)Point on graph: (0, 5)
Find the standard form of the equation of the hyperbola with the given characteristics.Vertices: (0, ±4)Asymptotes: y = ±2x
Find the standard form of the equation of the hyperbola with the given characteristics.Vertices: (±1, 0)Asymptotes: y = ±5x
Find the standard form of the equation of the ellipse with the given characteristics.Center: (1, 2)Major axis: verticalPoints on the ellipse:(1, 6), (3, 2)
Find the standard form of the equation of the ellipse with the given characteristics.Center: (0, 0)Major axis: horizontalPoints on the ellipse:(3, 1), (4, 0)
Find the standard form of the equation of the ellipse with the given characteristics.Foci: (0, ±9)Major axis length: 22

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