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mathematics
calculus 10th edition
Calculus 10th Edition Ron Larson, Bruce H. Edwards - Solutions
In Exercises find the intervals of convergence of (a) ƒ(x), (b) ƒ'(x),(c) ƒ"(x), (d) ∫ ƒ(x) dx. Include a check for convergence at the endpoints of the interval. f(x) Σ n=1 (-1)₂+¹(x-4)n n
In Exercises find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) n=0 (x - 2)" 2n
In Exercises find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) ~ n!(x − 2)n n=0
In Exercises(a) Write the repeating decimal as a geometric series(b) Write its sum as the ratio of two integers.0.64̅
In Exercises find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) n=1 3n(x - 2) n
In Exercises find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) n=0 (-1)^(x - 2)" (n + 1)²
In Exercises find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) ∞o Σ (5x)" n=0
In Exercises find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) n=0 x 10/ n
In Exercises find the third-degree Taylor polynomial centered at c. f(x) = tan x, c = || 77 4
In Exercises find the third-degree Taylor polynomial centered at c. 3x f(x) = e=³x, c = 0
In Exercises use the Ratio Test or the Root Test to determine the convergence or divergence of the series. n=1 1.3.5 2.5.8. . . (2n-1) (3n-1)
In Exercises find the nth Maclaurin polynomial for the function. f(x) = cos TX, n = 4
In Exercises find the nth Maclaurin polynomial for the function. f(x) = e-²x, n = 3 e-2r
In Exercises(a) Verify that the series converges(b) Use a graphing utility to find the indicated partial sum and complete the table(c) Use a graphing utility to graph the first 10 terms of the sequence of partial sums(d) Use the table to estimate the sum of the series n 5 10 15 20 25 S₂ 'n
In Exercises 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.e-0.25
In Exercises(a) Verify that the series converges(b) Use a graphing utility to find the indicated partial sum and complete the table(c) Use a graphing utility to graph the first 10 terms of the sequence of partial sums(d) Use the table to estimate the sum of the series n 5 10 15 20 25 S₂ 'n
In Exercises 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.cos(0.75)
In Exercises use the Ratio Test or the Root Test to determine the convergence or divergence of the series. n=1 n! en
In Exercises use the Ratio Test or the Root Test to determine the convergence or divergence of the series. 18 明
In Exercises find the vertex, focus, and directrix of the parabola, and sketch its graph.(x - 6)2 + 8(y + 7) = 0
In Exercises find the vertex, focus, and directrix of the parabola, and sketch its graph.y² = - 8x
In Exercises match the equation with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).](a)(b)(c)(d)(e)(f) 4 2 + -2 y -2- -4+ 2 4 6 X
In Exercises match the equation with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).](a)(b)(c)(d)(e)(f) 4 2 + -2 y -2- -4+ 2 4 6 X
In Exercises match the equation with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).](a)(b)(c)(d)(e)(f) 4 2 + -2 y -2- -4+ 2 4 6 X
In Exercises find the vertex, focus, and directrix of the parabola, and sketch its graph.(x + 5) + (y - 3)² = 0
In Exercises find the vertex, focus, and directrix of the parabola, and sketch its graph.x2 + бу = 0
In Exercises match the equation with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).](a)(b)(c)(d)(e)(f) 4 2 + -2 y -2- -4+ 2 4 6 X
In Exercises find the vertex, focus, and directrix of the parabola, and sketch its graph.y² + 4y + 8x - 12 = 0
In Exercises find the vertex, focus, and directrix of the parabola, and sketch its graph.x² + 4x + 4y -4 = 0
In Exercises find the vertex, focus, and directrix of the parabola, and sketch its graph.y2 + 6y + 8x + 25 = 0
In Exercises find the vertex, focus, and directrix of the parabola, and sketch its graph.y² - 4y - 4x = 0
In Exercises find the center, foci, vertices, and eccentricity of the ellipse, and sketch its graph.3x² + 7y² = 63
In Exercises find the center, foci, vertices, and eccentricity of the ellipse, and sketch its graph.16x² + y² = 16
In Exercises find an equation of the parabola.Directrix: y = -2; endpoints of latus rectum are (0, 2) and (8, 2).
In Exercises find an equation of the parabola.Axis is parallel to y-axis; graph passes through (0, 3), (3, 4), and (4, 11).
In Exercises find an equation of the parabola. Vertex: (2, 4) Points on the parabola: (0, 0), (4,0)
In Exercises find an equation of the parabola. Vertex: (0,4) Points on the parabola: (-2, 0), (2, 0)
In Exercises find an equation of the parabola. Vertex: Focus: (5, 4) (3, 4)
In Exercises find an equation of the parabola. Focus: (2, 2) Directrix: x = -2
In Exercises find an equation of the parabola. Vertex: (-2, 1) Focus: (-2,-1)
In Exercises find an equation of the parabola. Vertex: (0,5) Directrix: y = −3 -3
In Exercises find the center, foci, vertices, and eccentricity of the ellipse, and sketch its graph. (x − 3)² (y − 1)² + 16 25 = 1
In Exercises find the center, foci, vertices, and eccentricity of the ellipse, and sketch its graph. (x + 4)² + (y + 6)² 1/4 1
In Exercises find the center, foci, vertices, and eccentricity of the ellipse, and sketch its graph.9x² + 4y² + 36x - 24y + 36 = 0
In Exercises use the series representation of the function ƒ to find (if it exists). lim f(x) x-0
In Exercises find the Maclaurin series for the function. Use the table of power series for elementary functions.ƒ(x) = In(x - 1)
In Exercises find the Maclaurin series for the function. Use the table of power series for elementary functions.ƒ(x) = cos 3x
In Exercises find the Maclaurin series for the function. Use the table of power series for elementary functions.ƒ(x) = sin 2x
In Exercises find the Maclaurin series for the function. Use the table of power series for elementary functions.ƒ(x) = e6x
In Exercises match the equation with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).](a)(b)(c)(d)(e)(f)(x + 4)² = 2(y - 2) 4 2 + -2 y -2- -4+ 2 4 6 X
In Exercises match the equation with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).](a)(b)(c)(d)(e)(f)y² = 4x 4 2 + -2 y -2- -4+ 2 4 6 X
In Exercises use the series representation of the function ƒ to find (if it exists). lim f(x) x-0
In Exercises use the definition of Taylor series to find the Taylor series, centered at c, for the function. h(x) = 1 (1 + x)³¹ c=0
In Exercises use the definition of Taylor series to find the Taylor series, centered at c, for the function. g(x) = 5/1 + x, c = 0
In Exercises use the definition of Taylor series to find the Taylor series, centered at c, for the function. f(x) = √√√x₂ c = 4 x,
In Exercises find the sum of the convergent series by using a well-known function. Identify the function and explain how you obtained the sum. Σ n=1 (−1)n+1 1 4η η
In Exercises use the definition of Taylor series to find the Taylor series, centered at c, for the function. f(x) = CSC X, c= 2 (first three terms)
In Exercises use the definition of Taylor series to find the Taylor series, centered at c, for the function. f(x) = 1 / / X C = -1
In Exercises use the definition of Taylor series to find the Taylor series, centered at c, for the function. f(x) = 3x, c = 0
In Exercises find the sum of the convergent series by using a well-known function. Identify the function and explain how you obtained the sum. 1 32n+1(2n + 1)! Σ (-1). n=0
In Exercises find the sum of the convergent series by using a well-known function. Identify the function and explain how you obtained the sum. n=0 1 2n n!
In Exercises find the sum of the convergent series by using a well-known function. Identify the function and explain how you obtained the sum. 22n Σ(-1). 32n(2n)! n=0
In Exercises find the sum of the convergent series by using a well-known function. Identify the function and explain how you obtained the sum. n=1 (−1)n+1 1 5n n
In Exercises use the definition of Taylor series to find the Taylor series, centered at c, for the function. f(x) = cos x, C = TT 4
In Exercises use the definition of Taylor series to find the Taylor series, centered at c, for the function. f(x) = sin x, c = 3 T 4
In Exercises find the sum of the convergent series by using a well-known function. Identify the function and explain how you obtained the sum. n=0 2n 3″ n!
In Exercises find a power series for the function, centered at c, and determine the interval of convergence. f(x) = 1 3 - 2x² c=0
In Exercises find a power series for the function, centered at c, and determine the interval of convergence. f(x) 6 4 - x' C = 1
In Exercises find a geometric power series, centered at 0, for the function. h(x) = 3 2 + x
In Exercises(a) Write the repeating decimal as a geometric series(b) Write its sum as the ratio of two integers.0.09̅
In Exercises find the sum of the convergent series. Π 1 Σ (3) - (n + 1)(n + 2) n=0
In Exercises find the sum of the convergent series. Σ [(0.6)" + (0.8)"] n=1
In Exercises find the sum of the convergent series. 18 n=0 n
In Exercises find the sum of the convergent series. 18 3n+2 7 n=0 n
In Exercises(a) Use a graphing utility to find the indicated partial sum Sn and complete the table(b) Use a graphing utility to graph the first 10 terms of the sequence of partial sums. n Sn 5 10 15 20 25
In Exercises(a) Use a graphing utility to find the indicated partial sum Sn and complete the table(b) Use a graphing utility to graph the first 10 terms of the sequence of partial sums. n Sn 5 10 15 20 25
In Exercises find the sequence of partial sums S₁, S₂, S3, S4, and S5. 3+ +1 + 314 + لام +
In Exercises find the sequence of partial sums S₁, S₂, S3, S4, and S5. 1 1 + 2 4 - + 8 1 16 1 32 +
In Exercises(a) Use a graphing utility to find the indicated partial sum Sn and complete the table(b) Use a graphing utility to graph the first 10 terms of the sequence of partial sums. n Sn 5 10 15 20 25
In Exercises(a) Use a graphing utility to find the indicated partial sum Sn and complete the table(b) Use a graphing utility to graph the first 10 terms of the sequence of partial sums. n Sn 5 10 15 20 25
In Exercises determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an = √n+1 = √n
In Exercises determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an || n In n
(a) Determine the convergence or divergence of the series(b) Determine the convergence or divergence of the series 18 n=1 1 2n
In Exercises determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an sin √n √n
In Exercises determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an = n n² + 1
In Exercises determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. a n 1 n
In Exercises use a graphing utility to graph the first 10 terms of the sequence. 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 5n + 2 n
In Exercises determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an n³ + 1 n²
Consider an idealized population with the characteristic that each member of the population produces one offspring at the end of every time period. Each member has a life span of three time periods and the population begins with 10 newborn members. The following table shows the population during
Derive each identity using the appropriate geometric series.(a)(b) 1 0.99 1.01010101..
In Exercises determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an = 3 = 2 n² - 1
In Exercises determine the convergence or divergence of the sequence with the given nth term. If the sequence converges, find its limit. an = 2/5 n + 5
Let {an} be a sequence of positive numbers satisfyingProve that the seriesconverges. 1 lim (a)¹/n = L < r > 0. -
For what values of the positive constants a and b does the following series converge absolutely? For what values does it converge conditionally? + 010 1 + T + 4-3 + -
In Exercises use a graphing utility to graph the first 10 terms of the sequence. 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 = sin NTT 2
(a) Consider the following sequence of numbers defined recursively.Write the decimal approximations for the first six terms of this sequence. Prove that the sequence converges, and find its limit.(b) Consider the following sequence defined recursively byProve that this sequence converges, and find
In Exercises match the sequence with its graph. [The graphs are labeled (a), (b), (c), and (d).](a)(b)(c)(d) 9 an 5 4 3 2- I ترا 2 u ||||||| 4 6 8 10
The graph of the functionis shown below. Use the Alternating Series Test to show that the improper integralconverges. f(x) = 1, sin x X x = 0 x > 0
In Exercises match the sequence with its graph. [The graphs are labeled (a), (b), (c), and (d).](a)(b)(c)(d) 9 an 5 4 3 2- I ترا 2 u ||||||| 4 6 8 10
(a) Find a power series for the functioncentered at 0. Use this representation to find the sum of the infinite series(b) Differentiate the power series forUse the result to find the sum of the infinite series f(x) = xex
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