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Use the fact that Due in 23 minutes cos(w) - cos(w) = 2 (- 1)"w2n (2n)!...
22 . . 23 . 24 Use the binomial series to expand the function as a...
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Use the binomial series to expand the function as a power series. 7 (4 + x) 3 Σ Your answer cannot be understood or graded. More Information n = 0 X State the radius of convergence, R. R = 4 Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = x cos(4x) D) n = 0 Evaluate the indefinite integral as an infinite series. I conte...
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...
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
plz show work 1. (a) Find T5(x), the Taylor polynomial of degree 5, for Inx centered...
plz
show work
1. (a) Find T5(x), the Taylor polynomial of degree 5, for Inx centered at x = 1. (b) Evaluate Ts (3). How close is its value to In 3? (c) The interval of convergence for the Taylor series of In x centered at x= 1 is (0,2). Use the fact that Inx= - In to find a different value of x to use in Ts(x) to approximate In 3. How close is your approximation? 2. Long ago,...
Q5.1 8 Points 05.16 Show that of arctan x3 - dx = € (-1/n+1 23(2n –...
Q5.1 8 Points 05.16 Show that of arctan x3 - dx = € (-1/n+1 23(2n – 1)2 2 Q5.2 8 Points Determine at least how many terms of the series in part Q5.1 should be added up to approximate the value of - dx with an error less than "Jo X arctan x3 300
How to do part (c) and part(d）? How to do part (c) and part(d）? (a) Evaluate the integral 2 48 dx Your answer should be in the form kr, where k is an integer. What is the value of k? darctan(x dx r2...
How to do part (c) and part(d）?
How to do part (c) and part(d）?
(a) Evaluate the integral 2 48 dx Your answer should be in the form kr, where k is an integer. What is the value of k? darctan(x dx r2+1 (b) Now, lets evaluate the same integral using power series. First, find the power series for the function f(x)-Then, integrate it from o to 2, and call it S. S should be an infinite series. What are...
Matlab Help I understand and already did 2a. Need help with the Matlab part (2b). 2....
Matlab Help
I understand and already did 2a. Need help with the Matlab part
(2b).
2. (15 points) The Maclaurin series expansion of sin(x) is given by 3 sin)39 estimate the true value of sin(T/3). Calculate the truncation error (true percent relative error). (error between current and previous estimate) falls below 0.01%. Document the final value, the (a) Use the first three terms in this equation to calculate the value of sin(T/3). Use your calculator to (b) Now write a...
Question 2, non-calculator Question 1, calculator The curve C in the x-y-plane is given parametrically by (x(t), y(t), where dr = t sine) and dv = cos| t The Maclaruin series for a function f is give...
Question 2, non-calculator Question 1, calculator The curve C in the x-y-plane is given parametrically by (x(t), y(t), where dr = t sine) and dv = cos| t The Maclaruin series for a function f is given by r" for 1 sts 6 a) Use the ratio test to find the interval of convergence of the Maclaurin series for f a) Find the slope of the line tangent to the curve C at the point where t 3. b) Let...
THE CODE NEEDS TO BE ON MATLAB 2. Exercise (a) Let's write a script file that...
THE CODE NEEDS TO BE ON MATLAB
2. Exercise (a) Let's write a script file that calculates exp(2) by a Maclaurin series using a while loop exp x )=-+-+-+-+ The while loop should add each of the series terms. The program error as defined below is smaller than 0.01. Error is the exact value (i.e. exp(2)), minus the approximate value (i.e., the current series sum) should exit the loop when the absolute absolute error-lexact-approx Use fprintf within the loop such...
Let f(x) = cos(x2). Use (a) the Trapezoidal Rule and (b) the Midpoint Rule to approximate...
Let f(x) = cos(x2). Use (a) the Trapezoidal Rule and (b) the Midpoint Rule to approximate the integral ſo'f(x) dx with n = 8. Give each answer correct to six decimal places. To Mg = (c) Use the fact that IF"(x) = 6 on the interval [0, 1] to estimate the errors in the approximations from part (a). Give each answer correct to six decimal places. Error in Tg = Error in Mg = (d) Using the information in part...
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Use the binomial series to expand the function as a power series. 7 (4 + x) 3 Σ Your answer cannot be understood or graded. More Information n = 0 X State the radius of convergence, R. R = 4 Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = x cos(4x) D) n = 0 Evaluate the indefinite integral as an infinite series. I conte...
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...
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
plz
show work
1. (a) Find T5(x), the Taylor polynomial of degree 5, for Inx centered at x = 1. (b) Evaluate Ts (3). How close is its value to In 3? (c) The interval of convergence for the Taylor series of In x centered at x= 1 is (0,2). Use the fact that Inx= - In to find a different value of x to use in Ts(x) to approximate In 3. How close is your approximation? 2. Long ago,...
Q5.1 8 Points 05.16 Show that of arctan x3 - dx = € (-1/n+1 23(2n – 1)2 2 Q5.2 8 Points Determine at least how many terms of the series in part Q5.1 should be added up to approximate the value of - dx with an error less than "Jo X arctan x3 300
How to do part (c) and part(d）?
How to do part (c) and part(d）?
(a) Evaluate the integral 2 48 dx Your answer should be in the form kr, where k is an integer. What is the value of k? darctan(x dx r2+1 (b) Now, lets evaluate the same integral using power series. First, find the power series for the function f(x)-Then, integrate it from o to 2, and call it S. S should be an infinite series. What are...
Matlab Help
I understand and already did 2a. Need help with the Matlab part
(2b).
2. (15 points) The Maclaurin series expansion of sin(x) is given by 3 sin)39 estimate the true value of sin(T/3). Calculate the truncation error (true percent relative error). (error between current and previous estimate) falls below 0.01%. Document the final value, the (a) Use the first three terms in this equation to calculate the value of sin(T/3). Use your calculator to (b) Now write a...
Question 2, non-calculator Question 1, calculator The curve C in the x-y-plane is given parametrically by (x(t), y(t), where dr = t sine) and dv = cos| t The Maclaruin series for a function f is given by r" for 1 sts 6 a) Use the ratio test to find the interval of convergence of the Maclaurin series for f a) Find the slope of the line tangent to the curve C at the point where t 3. b) Let...
THE CODE NEEDS TO BE ON MATLAB
2. Exercise (a) Let's write a script file that calculates exp(2) by a Maclaurin series using a while loop exp x )=-+-+-+-+ The while loop should add each of the series terms. The program error as defined below is smaller than 0.01. Error is the exact value (i.e. exp(2)), minus the approximate value (i.e., the current series sum) should exit the loop when the absolute absolute error-lexact-approx Use fprintf within the loop such...
Let f(x) = cos(x2). Use (a) the Trapezoidal Rule and (b) the Midpoint Rule to approximate the integral ſo'f(x) dx with n = 8. Give each answer correct to six decimal places. To Mg = (c) Use the fact that IF"(x) = 6 on the interval [0, 1] to estimate the errors in the approximations from part (a). Give each answer correct to six decimal places. Error in Tg = Error in Mg = (d) Using the information in part...
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