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mathematics
precalculus
Thomas Calculus Early Transcendentals 13th Edition Joel R Hass, Christopher E Heil, Maurice D Weir - Solutions
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. an || 1 - из .. 70 4n²
Which of the series converge absolutely, which converge conditionally, and which diverge? Give reasons for your answers. Σ n=3 In n In (In n)
Which of the series converge, and which diverge? Give reasons for your answers. Στη sin n n=1 -- n
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. 8 n=1 (-100)" n!
Use any method to determine if the series converges or diverges. Give reasons for your answer. n=1 n ln n (-2)"
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. n+ 3 n² + 5n+6 = an
Which of the series converge absolutely, which converge conditionally, and which diverge? Give reasons for your answers. x n=1 In n n³
(a) Find the series’ radius and interval of convergence. For what values of x does the series converge (b) Absolutely, (c) Conditionally? 8 n=1 (3x + 1)n+1 2n + 2
Which of the series converge, and which diverge? Give reasons for your answers. 1 n=1n(1 + In²n)
Which of the series converge, and which diverge? Give reasons for your answers. 8 n=3 (1/n) (Inn) Vln²n – 1 -
Use any method to determine if the series converges or diverges. Give reasons for your answer. ∞ n=1 en ne
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. 1 - 5nª 4 n² + 8n³ = an
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. 00 n Σ(1)". n + 1 n=1
Find the Taylor series generated by ƒ at x = a.ƒ(x) = √x + 1, a = 0
(a) Find the series’ radius and interval of convergence. For what values of x does the series converge (b) Absolutely, (c) Conditionally? 8 n=1 (4x - 5)2n+1 ,3/2 n
Find the first four nonzero terms in the Maclaurin series for the function.cos2 x · sin x
Which of the series converge absolutely, which converge conditionally, and which diverge? Give reasons for your answers. ∞ 1 Σ =2 n (Inn)2
Use any method to determine if the series converges or diverges. Give reasons for your answer. Σ n=1 η n n
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. an 2n + 1 1-3√n
Find the Taylor series generated by ƒ at x = a.ƒ(x) = cos (2x + (π/2)), a = π/4
What are the Taylor series for 1/(1 - x), 1/(1 + x), ex, sin x, cos x, ln(1 + x), and tan-1x? How do you estimate the errors involved in replacing these series with their partial sums?
Find the first four nonzero terms in the Maclaurin series for the function.(tan-1 x)2
Find the Taylor series generated by ƒ at x = a.ƒ(x) = 2x, a = 1
How can you sometimes use power series to estimate the values of nonelementary definite integrals? To find limits?
Which of the series converge, and which diverge? Give reasons for your answers. n n=1n² + 1
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. 8 n=1 (-1)n+1(n!)² (2n)!
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 (tan (n) – tan (n − 1)) n=1
Which of the series converge absolutely, which converge conditionally, and which diverge? Give reasons for your answers. n=1 (-3)" n!
Use the Taylor series generated by ex at x = a to show that et= ea 1 + (x a) + - - (x − a)² 2! ..].
Use any method to determine if the series converges or diverges. Give reasons for your answer. n! Σ (2n + 1)! n=1
Find the series’ radius of convergence. n=1 n! 3.6.9.3n -Xn
Which of the series converge, and which diverge? Give reasons for your answers. W n=1 8 tan-¹ n 1 + n²
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. an n+ - (₁2/1¹) (₁ - 1) = 1 2n
Which of the series converge absolutely, which converge conditionally, and which diverge? Give reasons for your answers. n=1 (-1)^(n² + 1) 2n² + n - 1
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. Σ n=1 (−1)"(n + 1)" (2n)"
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 (in Vn + 1 - In Vn) n=1
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. a₁ = (-1² (1-1) an
(a) Find the series’ radius and interval of convergence. For what values of x does the series converge (b) Absolutely, (c) Conditionally? Σ(√n + 1 - √n)(x − 3)" - n=1
Use any method to determine if the series converges or diverges. Give reasons for your answer. Σ n=1 n2"(n + 1)! 3"n!
Which of the series converge, and which diverge? Give reasons for your answers. 8 n=1 2 1 + en
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. z(I + u) (-)3
Which of the series converge absolutely, which converge conditionally, and which diverge? Give reasons for your answers. Σ n=1 n + 1 n!
For approximately what values of x can you replace sin x by x - (x3/6) with an error of magnitude no greater than 5 * 10-4 ? Give reasons for your answer.
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. ∞ Σ n=1 COS NT n
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. an 1 + (−1)n -1 =
Find the first three nonzero terms of the Maclaurin series for each function and the values of x for which the series converges absolutely.ƒ(x) = x sin2 x
Use any method to determine if the series converges or diverges. Give reasons for your answer. (n + 3)! Σ 3!n!3m n=1
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. IM8 COS NTT nVn Σ n=1 n
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=1 n 1 n+ 1
(a) Find the series’ radius and interval of convergence. For what values of x does the series converge (b) Absolutely, (c) Conditionally? Σ n=1 1 + 2 + 3 + + n + 2² + 3² + ... + n².
Use any method to determine if the series converges or diverges. Give reasons for your answer. ∞ Σe="(m3) n=1
Which of the series converge, and which diverge? Give reasons for your answers. 85 n=1 en 1 + e²n
Estimate the error if P4(x) = 1 + x + (x2/2) + (x3/6) + (x4/24) is used to estimate the value of ex at x = 1/2.
Which of the series converge absolutely, which converge conditionally, and which diverge? Give reasons for your answers. Σ n=1 (-1)¹¹3n² n3 + 1
Which of the series converge, and which diverge? Give reasons for your answers. Σ n tan n=1 n
Find the first three nonzero terms of the Maclaurin series for each function and the values of x for which the series converges absolutely.ƒ(x) = (sin x) ln(1 + x)
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. 00 Σ n=1 (-1)n-1 n? + 2n + 1 ₂2
(a) Find the series’ radius and interval of convergence. For what values of x does the series converge (b) Absolutely, (c) Conditionally? n=1 3.5.7.(2n + 1) n². 2n -Xn+1
Estimate the error if P3(x) = x - (x3/6) is used to estimate the value of sin x at x = 0.1.
Which of the series converge absolutely, which converge conditionally, and which diverge? Give reasons for your answers. (-1)" Σ n=1h n=inV + 1
Find the first three nonzero terms of the Maclaurin series for each function and the values of x for which the series converges absolutely.ƒ(x) = (1 - x + x2)ex
(a) Find the series’ radius and interval of convergence. For what values of x does the series converge (b) Absolutely, (c) Conditionally? Σ n=1 1 2.4.6. (2n)
Use any method to determine if the series converges or diverges. Give reasons for your answer. n=1 (n + 1)(n + 2) n!
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. An n²2 - 2n + 1 n - 1
Find the first four nonzero terms in the Maclaurin series for the function.sin (tan-1 x)
Find the first three nonzero terms of the Maclaurin series for each function and the values of x for which the series converges absolutely.ƒ(x) = cos x - (2/(1 - x))
Find the first four nonzero terms in the Maclaurin series for the function.esin x
Use any method to determine if the series converges or diverges. Give reasons for your answer. Σ n=2 -n (Inn)"
Which of the series converge, and which diverge? Give reasons for your answers. n=1 sech n
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. (2n)! Σ(1)", 2"n!n n=1
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. an (−1)n +1 2n 1
Find the series’ radius of convergence. 8 Σ n=1 (n!)² 2" (2n)! τη
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. 8 n=1 (co COS ¹ ( 1₁1 + 1) - 1 = (₁ + + + ₂)) n+ 2 COS
Which of the series converge absolutely, which converge conditionally, and which diverge? Give reasons for your answers. n=1 2n 3n nn
Use any method to determine if the series converges or diverges. Give reasons for your answer. M8 Σ n=1 n! (=n)"
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. (2-2)(3+2) = an
Find the series’ radius of convergence. n=1 2.4.6 (2n) 2₁) ² x ² 2.5.8 (3n - 1)/
How close is the approximation sin x = x when |x| < 10-3 ? For which of these values of x is x < sin x?
If cos x is replaced by 1 - (x2/2) and |x| < 0.5, what estimate can be made of the error? Does 1 - (x2/2) tend to be too large, or too small? Give reasons for your answer.
Which of the series converge absolutely, which converge conditionally, and which diverge? Give reasons for your answers. 1 Σ n=1 Vn(n + 1)(n + 2)
For what values of a, if any, do the series converge? n=3 1 (! n 1 2a n+ 1
Use the identity sin2 x = (1 - cos 2x)/2 to obtain the Maclaurin series for sin2 x. Then differentiate this series to obtain the Maclaurin series for 2 sin x cos x. Check that this is the series for sin 2x.
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. Σ(1)"(Vn + Vn - νη) η n=1
Use Table 10.1 to find the sum of each series. 1 3² 4².2! + 34 44.4! 36 46.6! +
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. f(x) = 1/V1x²
Use Table 10.1 to find the sum of each series. 3 4 5 6 (+)² + ( )* + (+)³ + (¦ ) * · · · · + 4 4 4 4
Find the sum of each series 40n Σ n=1 (2n – 1)2(2n + 1)2
Use any method to determine if the series converges or diverges. Give reasons for your answer. n=1 (-3) 32
(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. M8 n=1 (x - 1)2 -2 (2n − 1)!
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. an || 1 (0.9)n
Use Theorem 20 to find the series’ interval of convergence and, within this interval, the sum of the series as a function of x. Σ (er – 4)" n=0
When x < 0, the series for ex is an alternating series. Use the Alternating Series Estimation Theorem to estimate the error that results from replacing ex by 1 + x + (x2/2) when -0.1 < x < 0. Compare your estimate with the one you obtained in Exercise 41.Data from in Exercise 41.The
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. Σ(−1)″ (√n² + n − n) n=1
Find the sum of each series 18 Σ (2η n=1 - 6 1)(2n + 1)
Use Table 10.1 to find the sum of each series. 1 + 1 + 1 1 + + + 2! 3! 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 (x + 4)n n3"
Use any method to determine if the series converges or diverges. Give reasons for your answer. IM n=1 n! Inn n(n + 2)!
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) = esin x
Which of the sequences {an} converge, and which diverge? Find the limit of each convergent sequence. an = 2n Vn+ 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. ∞ Σ 3"x" n=0
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