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study help
mathematics
precalculus
Thomas Calculus Early Transcendentals 13th Edition Joel R Hass, Christopher E Heil, Maurice D Weir - Solutions
Which of the sequences whose nth terms appear converge, and which diverge? Find the limit of each convergent sequence. an || n n 5 n
Use power series operations to find the Taylor series at x = 0 for the function.xex
Write out the first eight terms of each series to show how the series starts. Then find the sum of the series or show that it diverges. 8 Σ n=0 5 2n 3n
(a) Find the series’ radius and interval of convergence. For what values of x does the series converge (b) Absolutely, (c) Conditionally? 8 n=0 3nxn n!
Taylor’s formulaexpresses the value of ƒ at x in terms of the values of ƒ and its derivatives at x = a. In numerical computations, we therefore need a to be a point where we know the values of ƒ and its derivatives. We also need a to be close enough to the values of ƒ we are interested in to
What happens if you add a finite number of terms to a convergent series? A divergent series? What happens if you delete a finite number of terms from a convergent series? A divergent series?
Gives the first term or two of a sequence along with a recursion formula for the remaining terms. Write out the first ten terms of the sequence.a1 = a2 = 1, an+2 = an+1 + an
Find the binomial series for the function.(1 + x)4
Use the Root Test to determine if each series converges absolutely or diverges. n+1 Σ (-¹n ( ² + + + ))*+ ¹ n n=1
How do you reindex a series? Why might you want to do this?
Determine if the alternating series converges or diverges. Some of the series do not satisfy the conditions of the Alternating Series Test. Σ(-1)+1 n=1 Vn+ 1 n+ 1
Use power series operations to find the Taylor series at x = 0 for the function. x2 2 1 + cos x
Which of the sequences whose nth terms appear converge, and which diverge? Find the limit of each convergent sequence. = a, 1 + n -n
Which of the series converge, and which diverge? Give reasons for your answers. n=1 n n + 1
Write out the first eight terms of each series to show how the series starts. Then find the sum of the series or show that it diverges. Σ ( M8 n=0 + (-1) 5n
(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 4x2n n
Taylor’s formulaexpresses the value of ƒ at x in terms of the values of ƒ and its derivatives at x = a. In numerical computations, we therefore need a to be a point where we know the values of ƒ and its derivatives. We also need a to be close enough to the values of ƒ we are interested in to
Use the Root Test to determine if each series converges absolutely or diverges. -8 Σ n=1 (3 + (1/n))2n
Use the Limit Comparison Test to determine if each series converges or diverges. M8 Σ n=1 5n η 4η
Which of the sequences whose nth terms appear converge, and which diverge? Find the limit of each convergent sequence. an = n 3n n
Gives the first term or two of a sequence along with a recursion formula for the remaining terms. Write out the first ten terms of the sequence.a1 = 2, a2 = -1, an+2 = an+1/an
Determine if the alternating series converges or diverges. Some of the series do not satisfy the conditions of the Alternating Series Test. Σ(-1)n+1 n=1 3Vn+1 [ + u^
Find the binomial series for the function.(1 + x2)3
Which of the series converge, and which diverge? Give reasons for your answers. n=1 5 n + 1
Use the Limit Comparison Test to determine if each series converges or diverges. 8 Σ n=1 2n + 3 5η + 4 1
Write out the first eight terms of each series to show how the series starts. Then find the sum of the series or show that it diverges. Σ n=0 2n+1 5n
Use power series operations to find the Taylor series at x = 0 for the function. sin x - x + x³ 3!
(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 (x - 1)n n³ 3n
Under what circumstances will an infinite series of nonnegative terms converge? Diverge? Why study series of nonnegative terms?
Find the binomial series for the function. 1 X 2 4
Determine if the geometric series converges or diverges. If a series converges, find its sum. 1 + 25 + + + 4 +...
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. Σ(-1)"+1(0.1)" n=1
Which of the sequences whose nth terms appear converge, and which diverge? Find the limit of each convergent sequence. an 3 n 1/n
Find the binomial series for the function.(1 - 2x)3
Use the Limit Comparison Test to determine if each series converges or diverges. Σ n=2 Inn
(a) Find the series’ radius and interval of convergence. For what values of x does the series converge (b) Absolutely, (c) Conditionally? ∞ Σ n=0 xn vi + 3
Which of the series converge, and which diverge? Give reasons for your answers. n=1 3 √n
Use the Root Test to determine if each series converges absolutely or diverges. Σ+1(1-1) n=1 n?
What is the Integral Test? What is the reasoning behind it? Give an example of its use.
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. α Σ(1)"+1 n=1 (0.1)n n
Which of the sequences whose nth terms appear converge, and which diverge? Find the limit of each convergent sequence. an = n(2¹/n - 1)
Which of the series converge, and which diverge? Give reasons for your answers. ∞ -2 n=1n√n
Use series to estimate the integrals’ values with an error of magnitude less than 10-5. -0.6 sin x² dx
Determine if the geometric series converges or diverges. If a series converges, find its sum. 1 + (−3) + (−3)² + (−3)³ + (−3)4 + · ..
Use the Limit Comparison Test to determine if each series converges or diverges. Sin In[ 1 + n=1 1 n?
(a) Find the series’ radius and interval of convergence. For what values of x does the series converge (b) Absolutely, (c) Conditionally? n=0 (-1)"xn+1 √n + 3
Use power series operations to find the Taylor series at x = 0 for the function.x cos πx
Use the Root Test to determine if each series converges absolutely or diverges. 8 Σ n=2 (-1)" 1+n
When do p-series converge? Diverge? How do you know? Give examples of convergent and divergent p-series.
Let a and b be constants with 0 < a < b. Does the sequence {(an + bn)1/n} converge? If it does converge, what is the limit?
Find the sum of the infinite series 2 1 + + 10 + 3 10² 3 7 + 108 10⁹ + + 7 + 10³ 2 + 104 3 + 105 7 + 106 2 107
Determine if the geometric series converges or diverges. If a series converges, find its sum. 5 3 2 + 100 + ·100 +
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. 1 Σ(-1)". Vn n=1
Which of the sequences whose nth terms appear converge, and which diverge? Find the limit of each convergent sequence. an = W 2n + 1 +
Use series to estimate the integrals’ values with an error of magnitude less than 10-5. +0.4 0 ex - 1 X 1dx
Use power series operations to find the Taylor series at x = 0 for the function.x2 cos (x2)
(a) Find the series’ radius and interval of convergence. For what values of x does the series converge (b) Absolutely, (c) Conditionally? Σ n=0 n(x + 3)n 5n
Use any method to determine if the series converges or diverges. Give reasons for your answer. α να Σ n n=1 2n
Which of the series converge, and which diverge? Give reasons for your answers. Σ n=1 1 8n
Which of the series converge, and which diverge? Use any method, and give reasons for your answers. 1 Σ 3. ni2Vn + Vn n=1 +
What are the Direct Comparison Test and the Limit Comparison Test? What is the reasoning behind these tests? Give examples of their use.
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. 8 (-1)" Σ n=11+ √n
Which of the sequences whose nth terms appear converge, and which diverge? Find the limit of each convergent sequence. an (n + 1)! n!
Use series to estimate the integrals’ values with an error of magnitude less than 10-5. 0.5 0 1 V1 + x4 -dx
Determine if the geometric series converges or diverges. If a series converges, find its sum. 6 ข 4 ข +... + 3 + + + کر است
Show that if ∑∞n=1an converges, thenconverges. 8 n=1 (an))" 1+ sin (an) 2
Express each of the numbers as the ratio of two integers. 0.7 0.7777 . . . =
Use power series operations to find the Taylor series at x = 0 for the function. sin²x
Use power series operations to find the Taylor series at x = 0 for the function.cos2 x
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. 1 n + 3 V(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? 00 n=1 (2 + (-1)) (x + 1)¹−1
What are the Ratio and Root Tests? Do they always give you the information you need to determine convergence or divergence? Give examples.
Which of the series converge, and which diverge? Give reasons for your answers. n=l 2n 3”
Use power series operations to find the Taylor series at x = 0 for the function. 1 (1 − x)² -
Which of the series converge, and which diverge? Use any method, and give reasons for your answers. ∞ n=1 3n 2n 1
Find the sums of the serie. Σ n=1 9 (3η – 1)(3n + 2) -
Express each of the numbers as the ratio of two integers. 0.d = 0.dddd..., where d is a digit
What is an alternating series? What theorem is available for determining the convergence of such a series?
How can you estimate the error involved in approximating the sum of an alternating series with one of the series’ partial sums? What is the reasoning behind the estimate?
Use series to approximate the values of the integrals with an error of magnitude less than 10-8. 0 0.1 V1 + x^¹ dx
Which of the series converge, and which diverge? Use any method, and give reasons for your answers. 00 n + 1 Σ” n²√n n=1ht
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. ∞ Σ(1) n=1 sin n n²
Use power series operations to find the Taylor series at x = 0 for the function. 2 3 (1 − x)³
Which of the series converge, and which diverge? Give reasons for your answers. n=1 5n 4+3
Use any method to determine if the series converges or diverges. Give reasons for your answer. 8 n=1 n n 2 " - ²)" n
(a) Find the series’ radius and interval of convergence. For what values of x does the series converge (b) Absolutely, (c) Conditionally? (-1) Σ n=1 32n(x - 2)n Зи
Use series to approximate the values of the integrals with an error of magnitude less than 10-8. 0 1 cos x dx X x²
What do you know about rearranging the terms of an absolutely convergent series? Of a conditionally convergent series?
Which of the series converge absolutely, which converge, and which diverge? Give reasons for your answers. Σ(-1)+13 + n 5 + n τη 00 n=1
Find the sums of the serie. Σ n=3 (4n - -8 3)(4n + 1)
Express each of the numbers as the ratio of two integers. 0.06 0.06666...
Use any method to determine if the series converges or diverges. Give reasons for your answer. Σ n=1 2 + (-1)" 1.25"
Which of the series converge, and which diverge? Give reasons for your answers. n=0 -2 n + 1
(a) Find the series’ radius and interval of convergence. For what values of x does the series converge (b) Absolutely, (c) Conditionally? n Σ (¹ + A)". n n=1
What is a power series? How do you test a power series for convergence? What are the possible outcomes?
Find the value of a for which the limitis finite and evaluate the limit. sin (ax) - sin x sin x - x x3 lim x-0
How do you know that the functions sin x, ln x, and ex are not polynomials? Give reasons for your answer.
Find the sums of the serie. n Σεπ n=0
Use power series operations to find the Taylor series at x = 0 for the function.x tan-1 x2
What are the basic facts abouta. Sums, differences, and products of power series?b. Substitution of a function for x in a power series?c. Term-by-term differentiation of power series?d. Term-by-term integration of power series?Give examples.
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