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Q5.1 8 Points 05.16 Show that of arctan x3 - dx = € (-1/n+1 23(2n –...
3) Later in this course, we will learn that the function, arctan x, is equivalent to a power series for x on the interval -1sxs: 2n+1 (-1)" arctan x = We can use this power series to approxim...
3) Later in this course, we will learn that the function, arctan x, is equivalent to a power series for x on the interval -1sxs: 2n+1 (-1)" arctan x = We can use this power series to approximate the constant π . a) First, evaluate arctan1). (You do not need the series to evaluate it.) b) Use your answer from part (a) and the power series above to find a series representation for (The answer will be just a series-not...
Use the fact that Due in 23 minutes cos(w) - cos(w) = 2 (- 1)"w2n (2n)!...
Use the fact that Due in 23 minutes cos(w) - cos(w) = 2 (- 1)"w2n (2n)! to evaluate the following integral to within an error 0.01. cos(1.4.)dx. Estimate = Preview How many non-zero terms of the Maclaurin series did you use to approximate this integral? Preview Now estimate the error of the approximation. error < Preview
6. (2n) a. Use the AST to show this series converges. b. Approximate the sum by calculating s c. ...
6. (2n) a. Use the AST to show this series converges. b. Approximate the sum by calculating s c. Find a maximum for the absolute value of the error (error]) in this approximation. d. How many terms n must be added (i.e. s,) so that Jerrort .001
6. (2n) a. Use the AST to show this series converges. b. Approximate the sum by calculating s c. Find a maximum for the absolute value of the error (error]) in this approximation....
2. (a) Show that the series sin "2n Sman 1 ) converges n = 1 (b)...
2. (a) Show that the series sin "2n Sman 1 ) converges n = 1 (b) Find an estimate of the magnitude of the error if the sum of the series is calculated by summing up the first 20 terms of the series. [4+3=7 pts]
n, fx/<1/2n 5. In the interval (-17, T), O, (x) = jo, x]>1/2n (a) Expand 8,...
n, fx/<1/2n 5. In the interval (-17, T), O, (x) = jo, x]>1/2n (a) Expand 8, (x) as a Fourier cosine series. (b) Show that your Fourier series agree with a Fourier expansion of d(x) in the limit as n →00.
Consider the integral 1 To vita dx V1 + x3 (a) Write out the first four...
Consider the integral 1 To vita dx V1 + x3 (a) Write out the first four non-zero terms of the MacLaurin series for the above integral. (b) Write out the first four non-zero terms of the series for 1 so dx V1 + x3 (c) How many terms of the above series should we add together to estimate p1/2 dc V1 + x3 within 0.001? 1
In the following, we will tse a kmown power series to approximate 1/2 arctan(r) dr to within 0.00...
In the following, we will tse a kmown power series to approximate 1/2 arctan(r) dr to within 0.00001 of the actual value of the definite integral (a) [2pt] Use a known power series representation to express (ctan(x) as a Maclaurin series. What is the radius of the series convergence? 1/2 (b) [4pts] Use your answer from part (a) to express(r) dr as an alternating series (c) [6pts] Your series in part (b) will converge by the Alternating Series Test. (You...
(5 pts) Consider the series 8 W arctan(n) n6 n=1 (a) For all n > 1,...
(5 pts) Consider the series 8 W arctan(n) n6 n=1 (a) For all n > 1, 0 < arctan(x) < x2 Give the best possible bound. And so 0 < an arctan(n) = <bn n/(2n^6) Since 0 < an <bn, which of the following test should we apply? A. The integral test B. The comparison test. C. The nth term test for divergence D. The ratio test E. The limit comparison test F. The p-series test G. The root test...
Please show the work for each practical parts. Thanks 8. a) Write at least the first...
Please show the work for each practical parts.
Thanks
8. a) Write at least the first 4 terms of a Taylor(Maclaurin) Series centered at O for f(x)=es (Recall that in the previous question, you developed a series for $(x)=e) (7 pts.) b) Evaluate * dx using the series you generated in part a) (use 4 terms) (10pts) (4 pts.) c) Determine the approximate error of your answer in part b)
* This is for CS 101 Java class. I can only use "while" loops. I cannot...
* This is for CS 101 Java class. I can only use "while" loops. I
cannot use "for", "do-while" or any other repetition method.*
d. Create a new project Lab04d. In this part, you are going to compute arctan(x) in radians The following formula approximates the value of arctan(x) using Taylor series expansion: 2k +1 tan-1 (x) = > (-1)" 2k 1 k=0 Depending on the number of terms included in the summation the approximation becomes more accurate Your program...
3) Later in this course, we will learn that the function, arctan x, is equivalent to a power series for x on the interval -1sxs: 2n+1 (-1)" arctan x = We can use this power series to approximate the constant π . a) First, evaluate arctan1). (You do not need the series to evaluate it.) b) Use your answer from part (a) and the power series above to find a series representation for (The answer will be just a series-not...
Use the fact that Due in 23 minutes cos(w) - cos(w) = 2 (- 1)"w2n (2n)! to evaluate the following integral to within an error 0.01. cos(1.4.)dx. Estimate = Preview How many non-zero terms of the Maclaurin series did you use to approximate this integral? Preview Now estimate the error of the approximation. error < Preview
6. (2n) a. Use the AST to show this series converges. b. Approximate the sum by calculating s c. Find a maximum for the absolute value of the error (error]) in this approximation. d. How many terms n must be added (i.e. s,) so that Jerrort .001
6. (2n) a. Use the AST to show this series converges. b. Approximate the sum by calculating s c. Find a maximum for the absolute value of the error (error]) in this approximation....
2. (a) Show that the series sin "2n Sman 1 ) converges n = 1 (b) Find an estimate of the magnitude of the error if the sum of the series is calculated by summing up the first 20 terms of the series. [4+3=7 pts]
n, fx/<1/2n 5. In the interval (-17, T), O, (x) = jo, x]>1/2n (a) Expand 8, (x) as a Fourier cosine series. (b) Show that your Fourier series agree with a Fourier expansion of d(x) in the limit as n →00.
Consider the integral 1 To vita dx V1 + x3 (a) Write out the first four non-zero terms of the MacLaurin series for the above integral. (b) Write out the first four non-zero terms of the series for 1 so dx V1 + x3 (c) How many terms of the above series should we add together to estimate p1/2 dc V1 + x3 within 0.001? 1
In the following, we will tse a kmown power series to approximate 1/2 arctan(r) dr to within 0.00001 of the actual value of the definite integral (a) [2pt] Use a known power series representation to express (ctan(x) as a Maclaurin series. What is the radius of the series convergence? 1/2 (b) [4pts] Use your answer from part (a) to express(r) dr as an alternating series (c) [6pts] Your series in part (b) will converge by the Alternating Series Test. (You...
(5 pts) Consider the series 8 W arctan(n) n6 n=1 (a) For all n > 1, 0 < arctan(x) < x2 Give the best possible bound. And so 0 < an arctan(n) = <bn n/(2n^6) Since 0 < an <bn, which of the following test should we apply? A. The integral test B. The comparison test. C. The nth term test for divergence D. The ratio test E. The limit comparison test F. The p-series test G. The root test...
Please show the work for each practical parts.
Thanks
8. a) Write at least the first 4 terms of a Taylor(Maclaurin) Series centered at O for f(x)=es (Recall that in the previous question, you developed a series for $(x)=e) (7 pts.) b) Evaluate * dx using the series you generated in part a) (use 4 terms) (10pts) (4 pts.) c) Determine the approximate error of your answer in part b)
* This is for CS 101 Java class. I can only use "while" loops. I
cannot use "for", "do-while" or any other repetition method.*
d. Create a new project Lab04d. In this part, you are going to compute arctan(x) in radians The following formula approximates the value of arctan(x) using Taylor series expansion: 2k +1 tan-1 (x) = > (-1)" 2k 1 k=0 Depending on the number of terms included in the summation the approximation becomes more accurate Your program...
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