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5. Consider 2n=1,5 SOO a. Using the remainder theorem for the integral test, how many terms...
Exercise 1: Use the Taylor Remainder Theorem for the following (a) How many terms of the...
Exercise 1: Use the Taylor Remainder Theorem for the following (a) How many terms of the Maclaurin series are needed to approximatee to 0001 accuracy? (Use the M above.) (b) How many terms of the series are needed to approximato.0000001 accuracy? (Use the M above.) (c) How many terms of the series are needed to approximate e10 to .0001 accuracy. (Hint: you are trying to solve (I 0001)
To test the series e 2n for convergence, you can use the Integral Test. (This is...
To test the series e 2n for convergence, you can use the Integral Test. (This is also a geometric series, so we could n=1 also investigate convergence using other methods.) Find the value of e-24 dx = Preview Ji What does this value tell you about the convergence of the series e-2n? the series definitely diverges the series might converge or diverge: we need more information the series definitely converges Compute the value of the following improper integral, if it...
a,b,c and d (-1) 4. (3 points each) Consider the series n° +2n +3 (a) Prove...
a,b,c and d
(-1) 4. (3 points each) Consider the series n° +2n +3 (a) Prove that this series converges absolutely. (b) Show that this series satisfies all three conditions of the Alternating Series Test. HI11-2212, JL ILG-2020 Test #3 (c) What value of n guarantees that the partial sum 8, approximates the sum of this series to within an accuracy of 0.01? (d) Find the sum of the series with this accuracy (by finding the appropriate partial sum sn,...
Problem 3. Consider the series: 1 n [ln (n)]4 n=2 a) (6 pts) Use the integral...
Problem 3. Consider the series: 1 n [ln (n)]4 n=2 a) (6 pts) Use the integral test to show that the above series is convergent. b) (4 pts) How many terms do we need to add to approximate the sum within Error < 0.0004.
Question 11 0/5 points n+1 satisfies all requirements of the Alternating Series Test. (You don't It...
Question 11 0/5 points n+1 satisfies all requirements of the Alternating Series Test. (You don't It 2n=1 have to check that - trust me on this one.) (2n+1) (a) Use a calculator to evaluate the partial sum S3 of this series. Give the answer rounded to four decimal places. (b) Estimate the error of using S3 as an approximation to the sum of the series, i.e. estimate the remainder R3. Recall that the remainder estimate of the Alternating Series Test...
The series converges by the Alternating Series Test. Use Theorem 9.9: Error Bounds for Alternatin...
The series converges by the Alternating Series Test. Use Theorem
9.9: Error Bounds for Alternating Series to find how many terms
give a partial sum, Sn, within 0.01 of the sum, S, of
the series.
-1 I n Theorem 9.9: Error Bounds for Alternating Series Let n = Σ Suppose that 0 < an+1 < an for all n and limn-too an-0. Then (- 1)i-lai be the nth partial sum of an alternating series and let S = lim Sn....
I'm having difficulty how many terms need to be added in. Test the series for convergence...
I'm having difficulty how many terms need
to be added in.
Test the series for convergence or divergence. 00 Σ (-1)" n2n n = 1 Identify bn. 1 n2" Evaluate the following limit. lim bn n → 00 0 Since lim bn O and bn + 1 s bn for all n, the series is convergent n00 If the series is convergent, use the Alternating Series Estimation Theorem to determine how many terms we need to add in order to...
1. 2. (1 point) Consider the following convergent series: Suppose that you want to approximate the...
1.
2.
(1 point) Consider the following convergent series: Suppose that you want to approximate the value of this series by computing a partial sum, then bounding the error using the integral remainder estimate. In order to bound the value of the series between two numbers which are no more than 10 apart, what is the fewest number of terms of the series you would need? Fewest number of terms is 585 (1 point) Consider the following series: le(n Use...
5. (15 pts) Sinn a.) Apply the Divergence Test to this series. State your conclusion b.)...
5. (15 pts) Sinn a.) Apply the Divergence Test to this series. State your conclusion b.) Apply the Integral test. You should state the three conditions needed for c) but you may skip if possible, otherwise, say "no sum. 6. (20 pts) _ ( +1) a.) Determine converge diverge using one of the comparison tests. Justify every step b.) Find the correct partial fraction decomposition for a = Solve for the unknown constants in that partial fraction decomposition. C.) Rewrite...
Exercise 1: Use the Taylor Remainder Theorem for the following (a) How many terms of the Maclaurin series are needed to approximatee to 0001 accuracy? (Use the M above.) (b) How many terms of the series are needed to approximato.0000001 accuracy? (Use the M above.) (c) How many terms of the series are needed to approximate e10 to .0001 accuracy. (Hint: you are trying to solve (I 0001)
To test the series e 2n for convergence, you can use the Integral Test. (This is also a geometric series, so we could n=1 also investigate convergence using other methods.) Find the value of e-24 dx = Preview Ji What does this value tell you about the convergence of the series e-2n? the series definitely diverges the series might converge or diverge: we need more information the series definitely converges Compute the value of the following improper integral, if it...
a,b,c and d
(-1) 4. (3 points each) Consider the series n° +2n +3 (a) Prove that this series converges absolutely. (b) Show that this series satisfies all three conditions of the Alternating Series Test. HI11-2212, JL ILG-2020 Test #3 (c) What value of n guarantees that the partial sum 8, approximates the sum of this series to within an accuracy of 0.01? (d) Find the sum of the series with this accuracy (by finding the appropriate partial sum sn,...
Problem 3. Consider the series: 1 n [ln (n)]4 n=2 a) (6 pts) Use the integral test to show that the above series is convergent. b) (4 pts) How many terms do we need to add to approximate the sum within Error < 0.0004.
Question 11 0/5 points n+1 satisfies all requirements of the Alternating Series Test. (You don't It 2n=1 have to check that - trust me on this one.) (2n+1) (a) Use a calculator to evaluate the partial sum S3 of this series. Give the answer rounded to four decimal places. (b) Estimate the error of using S3 as an approximation to the sum of the series, i.e. estimate the remainder R3. Recall that the remainder estimate of the Alternating Series Test...
The series converges by the Alternating Series Test. Use Theorem
9.9: Error Bounds for Alternating Series to find how many terms
give a partial sum, Sn, within 0.01 of the sum, S, of
the series.
-1 I n Theorem 9.9: Error Bounds for Alternating Series Let n = Σ Suppose that 0 < an+1 < an for all n and limn-too an-0. Then (- 1)i-lai be the nth partial sum of an alternating series and let S = lim Sn....
I'm having difficulty how many terms need
to be added in.
Test the series for convergence or divergence. 00 Σ (-1)" n2n n = 1 Identify bn. 1 n2" Evaluate the following limit. lim bn n → 00 0 Since lim bn O and bn + 1 s bn for all n, the series is convergent n00 If the series is convergent, use the Alternating Series Estimation Theorem to determine how many terms we need to add in order to...
1.
2.
(1 point) Consider the following convergent series: Suppose that you want to approximate the value of this series by computing a partial sum, then bounding the error using the integral remainder estimate. In order to bound the value of the series between two numbers which are no more than 10 apart, what is the fewest number of terms of the series you would need? Fewest number of terms is 585 (1 point) Consider the following series: le(n Use...
5. (15 pts) Sinn a.) Apply the Divergence Test to this series. State your conclusion b.) Apply the Integral test. You should state the three conditions needed for c) but you may skip if possible, otherwise, say "no sum. 6. (20 pts) _ ( +1) a.) Determine converge diverge using one of the comparison tests. Justify every step b.) Find the correct partial fraction decomposition for a = Solve for the unknown constants in that partial fraction decomposition. C.) Rewrite...
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