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mathematics
precalculus
Calculus Of A Single Variable 11th Edition Ron Larson, Bruce H. Edwards - Solutions
For what values of a, if any, do the series converge? Σ n=1 α ( n + 2 1 n n + 4
The approximation ex = 1 + x + (x2/2) is used when x is small. Use the Remainder Estimation Theorem to estimate the error when |x| < 0.1.
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. Σ(-1)" (√n + 1 - Vn) n=1
Find the sum of each series n=1 (4n 4 - - 3)(4n + 1)
Suppose that ƒ(x) is differentiable on an interval centered at x = a and that g(x) = b0 + b1(x - a) + · · · + bn(x - a)n is a polynomial of degree n with constant coefficients b0, . . . , bn. Let E(x) = ƒ(x) - g(x). Show that if we impose on g the conditions.i) E(a) = 0ii)thenThus, the Taylor
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. an = 2 n
Which of the series converge absolutely, which converge conditionally, and which diverge? Give reasons for your answers. Σ n=2 nVm - 1 1 ₂2
Find the series’ radius of convergence. Σ n=1 ( n n + U ne
Use any method to determine if the series converges or diverges. Give reasons for your answer. IM8 n Σ n=2 (In n)(n/2)
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. (n!)23n Σ(1)", (2n + 1)! n=1
Which of the series converge, and which diverge? Give reasons for your answers. Σ sech²n n=1
The Taylor polynomial of order 2 generated by a twice-differentiable function ƒ(x) at x = a is called the quadratic approximation of ƒ at x = a. Find the (a) Linearization (Taylor polynomial of order 1) and (b) Quadratic approximation of ƒ at x = 0.ƒ(x) = ln (cos x)
Find a formula for the nth partial sum of the series and use it to determine if the series converges or diverges. If a series converges, find its sum. ∞ Σ(√n +4√n + 3) n=1
The estimate √1 + x = 1 + (x/2) is used when x is small. Estimate the error when |x| < 0.01.
Let ƒ(x) have derivatives through order n at x = a. Show that the Taylor polynomial of order n and its first n derivatives have the same values that ƒ and its first n derivatives have at x = a.
Use Table 10.1 to find the sum of each series. 1 - 3²x²2 2! + 34x4 4! 36x6 6! +.
Find the sum of each series Σ(tan-¹ (n) - tan-1¹(n + 1)) n=1
(a) Find the series’ radius and interval of convergence. Then identify the values of x for which the series converges (b) Absolutely and (c) Conditionally. 8 n=0 (n+1)x²n-1 3n
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. 1 + 1 4 1 9 - 1 16 1 + + 25 1 36 - 1 49 - 1 64 +
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. an = n 2"
Use Theorem 20 to find the series’ interval of convergence and, within this interval, the sum of the series as a function of x. M8 Σ n=0 1² +1 3 n
Use the equationto establish the following test. Let ƒ have continuous first and second derivatives and suppose that ƒ′(a) = 0. Thena. ƒ has a local maximum at a if ƒ″ ≤ 0 throughout an interval whose interior contains a;b. ƒ has a local minimum at a if ƒ″ ≥ 0 throughout an interval
Use Taylor’s formula with a = 0 and n = 3 to find the standard cubic approximation of ƒ(x) = 1/(1 - x) at x = 0. Give an upper bound for the magnitude of the error in the approximation when |x| ≤ 0.1.
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. 1 4 + 1 -100 6 8 1 1 + 10 12 1 14 +
Use Table 10.1 to find the sum of each series. •• + 9x + çx + bx + EX
Use Theorem 20 to find the series’ interval of convergence and, within this interval, the sum of the series as a function of x. ∞ n Σ(In x)" n=0
Find the sum of each series Σ n=1 1 In(n + 2) 1 In(n + 1)
(a) Find the series’ radius and interval of convergence. Then identify the values of x for which the series converges (b) Absolutely and (c) Conditionally. x Σ n=1 -n χ Γη
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. An || sin² n 2n
Find the sum of each series Σ n=1 21/n 1 21/(n+1)
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. 8 (-1)" cschn n=1
Use Table 10.1 to find the sum of each series. 2 3 1 23 33.3 + 25 35.5 27 37.7 +
(a) Find the series’ radius and interval of convergence. Then identify the values of x for which the series converges (b) Absolutely and (c) Conditionally. x n=1 Xn nn
Use Table 10.1 to find the sum of each series. TT 3 .3 TT 33.3! + TT5 35.5! 7 TT 37.7! +
Use Theorem 20 to find the series’ interval of convergence and, within this interval, the sum of the series as a function of x. F-1) Vx Σ 2 n=0 n
Show that if the graph of a twice-differentiable function ƒ(x) has an inflection point at x = a, then the linearization of ƒ at x = a is also the quadratic approximation of ƒ at x = a. This explains why tangent lines fit so well at inflection points.
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. (-1)" sech n n=1
Use Theorem 20 to find the series’ interval of convergence and, within this interval, the sum of the series as a function of x. n=0 (x + 1)2n 9n
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. an = sin n n
The Taylor polynomial of order 2 generated by a twice-differentiable function ƒ(x) at x = a is called the quadratic approximation of ƒ at x = a. Find the (a) Linearization (Taylor polynomial of order 1) (b) Quadratic approximation of ƒ at x = 0.ƒ(x) = tan x
Use any method to determine if the series converges or diverges. Give reasons for your answer. n=1 (2n + 3)(2n + 3) 3n+2
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. an = Nπ COS (NT)
Find the sum of each series Σ ( n=1 Vn 1 Vn + 1
(a) Find the series’ radius and interval of convergence. Then identify the values of x for which the series converges (b) Absolutely and (c) Conditionally. n=0 (n + 1)(2x + 1)" (2n + 1)2¹
Find the sum of each series 2n + 1 n(n + 1)2 Σ n=1 n(n
Use Table 10.1 to find the sum of each series. 1 1 2 2.2² 1 + 1 1 3.23 4.24 - +.
Are there any values of x for whichconverges? Give reasons for your answer. Ση=1(1/nx)
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. Σ |n=1 (-1)" √n + √n + 1
(a) Find the series’ radius and interval of convergence. Then identify the values of x for which the series converges (b) Absolutely and (c) Conditionally. n=1 (-1)-¹(3x - 1)" n²
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. an = ㅠ 2 n sin +
The Taylor polynomial of order 2 generated by a twice-differentiable function ƒ(x) at x = a is called the quadratic approximation of ƒ at x = a. Find the (a) Linearization (Taylor polynomial of order 1) and (b) Quadratic approximation of ƒ at x = 0.ƒ(x) = sin x
Use Theorem 20 to find the series’ interval of convergence and, within this interval, the sum of the series as a function of x. 8 n=0 (x - 1)2n 4n
Use any method to determine if the series converges or diverges. Give reasons for your answer. 8 Σ n=1 (n!)2 (2n)!
Use the identity cos2 x = cos 2x + sin2 x to obtain a power series for cos2 x.
The Taylor polynomial of order 2 generated by a twice-differentiable function ƒ(x) at x = a is called the quadratic approximation of ƒ at x = a. Find the (a) Linearization (Taylor polynomial of order 1) and (b) Quadratic approximation of ƒ at x = 0.ƒ(x) = cosh x
Use Theorem 20 to find the series’ interval of convergence and, within this interval, the sum of the series as a function of x. M8 X Σ 2 n=0 n
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. an || =
Use Table 10.1 to find the sum of each series. - I[X +6X = ₁x + çX - €X
(a) Find the series’ radius and interval of convergence. Then identify the values of x for which the series converges (b) Absolutely and (c) Conditionally. (−1)"(x Σ n=0 − 1)2n+1 - 2n + 1
Estimate the magnitude of the error involved in using the sum of the first four terms to approximate the sum of the entire series. Σ(-1)+1! n=1 n
Use Table 10.1 to find the sum of each series. -1 + 2x - 3x² + 4x³ - 5x4 +
Each of the series is the value of the Taylor series at x = 0 of a function ƒ(x) at a particular point. What function and what point? What is the sum of the series? 1 - 1/2 + 1/6 4 + (-1)". + · 1 4"
(a) Find the series’ radius and interval of convergence. Then identify the values of x for which the series converges (b) Absolutely and (c) Conditionally. n=1 (coth n).xn
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. an = In n In 2n
Use a geometric series to represent each of the given functions as a power series about x = 0, and find their intervals of convergence.a.b. f(x) = 5 3 - x
a. Let P be an approximation of π accurate to n decimals. Show that P + sin P gives an approximation correct to 3n decimals.b. Try it with a calculator.
Use Table 10.1 to find the sum of each series. x² - 2x³ + 2²x4 2! 2³x5 3! + 24x6 4!
Estimate the magnitude of the error involved in using the sum of the first four terms to approximate the sum of the entire series. 1 Σ(-1)+1. 10n n=1
(a) Find the series’ radius and interval of convergence. Then identify the values of x for which the series converges (b) Absolutely and (c) Conditionally. Σ(csch n)x¹ n=1
a. Use Taylor’s formula with n = 2 to find the quadratic approximation of ƒ(x) = (1 + x)k at x = 0 (k a constant).b. If k = 3, for approximately what values of x in the interval [0, 1] will the error in the quadratic approximation be less than 1 / 100?
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. an In (n + 1) Vn
Select the correct antiderivative. X Ide dx √√√x² + 1 (a) 2√√x² + 1 + C (c) √√√x² + 1 + C (b) √√x² +1+C (d) In(x² + 1) + C
Select the correct antiderivative. x² + 1 dx (a) In√√x² + 1 + C (c) arctanx+C 2x (x² + 1)² (d) In(x² + 1) + C (b) + C
What procedure should you use to fit each integrand to the basic integration rules? Do not integrate. (a) 2 + x dx ² +9 (b) fo cot² x dx
Select the basic integration formula you can use to find the indefinite integral, and identify u and a when appropriate. Do not integrate. 21 + 1 1²+1-4 at
Select the basic integration formula you can use to find the indefinite integral, and identify u and a when appropriate. Do not integrate. 1 √√x(12√√x) dx
Which integral requires more steps to find? Explain. Do not integrate. ∫sin8 x dx ∫sin8 x cos x dx
Describe how to integrate a rational function with a numerator and denominator of the same degree.
Evaluate the definite integral. Use a graphing utility to verify your result. 2 Jo x²e-2x dx
In your own words, describe how to choose u and dv when using integration by parts.
Describe the technique for finding ∫sec5 x tan7 x dx. Do not integrate.
Evaluate the definite integral. Use a graphing utility to verify your result. *1/2 0 arccos x dx
Evaluate the definite integral. Use a graphing utility to verify your result. Jo xex/2 dx
Evaluate the definite integral. Use a graphing utility to verify your result. Jo x arcsin x² dx
How can you use integration by parts on an integrand with a single term that does not fit any of the basic integration rules?
Evaluate the definite integral. Use a graphing utility to verify your result. "I S Jo et sin x dx
Evaluate the definite integral. Use a graphing utility to verify your result. Jo In(4 + x²) dx
Evaluate the definite integral. Use a graphing utility to verify your result. R/4 10 x cos 2x dx
Use the tabular method to find the indefinite integral. [ (1 − x) (e x + 1) dx
Find the indefinite integral using integration by parts with the given choices of u and dv.∫(7 - x)ex/2 dx; u = 7 - x, dv = ex/2 dx
Find the indefinite integral using integration by parts with the given choices of u and dv.∫(2x + 1) sin 4x dx; u = 2x + 1, dv = sin 4x dx
Find the general solution of the differential equation.y' = arctan x/2
Evaluate the definite integral. Use a graphing utility to verify your result. +4 x arcsec x dx
Evaluate the definite integral. Use a graphing utility to verify your result. n/8 x sec² 2x dx
Find the general solution of the differential equation.y' = tan3 3x sec 3x
Use the tabular method to find the indefinite integral. √ (6 + x) (6 + x)√√4x + 9 dx
Find the general solution of the differential equation.y' = √tan x sec4 x
Find the indefinite integral. Use a computer algebra system to confirm your result. 1 sec x tan x dx
Evaluate the definite integral. Use a graphing utility to verify your result. L₁ 5 (t + 2)¹¹ dt
Use the tabular method to find the indefinite integral. (x + 2)² sin x dx
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