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4. a) Find a power series for the function. f(x) =...
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...
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...
Find a power series representation for the function. f(x) = فيه (x – 4)2 00 f(x)...
Find a power series representation for the function. f(x) = فيه (x – 4)2 00 f(x) = Σ no Determine the radius of convergence, R. R = Evaluate the indefinite integral as a power series. Je at c+ Σ ΦΟ η = Ο What is the radius of convergence R? R = Find the radius of convergence, R, of the series. 3n Σ n! n=1 R= Find the interval, 1, of convergence of the series. (Enter your answer using interval...
15. . 16 . 17 Find a power series representation for the function. х f(x) (1...
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Find a power series representation for the function. х f(x) (1 + 6x)2 f(x) = ( (-6).*- 1 nxt n = 0 x Determine the radius of convergence, R. R = 1/6 Evaluate the indefinite integral as a power series. t Vi dt 1 - 79 C+ Σ Σ( n = 0 What is the radius of convergence R? R= Use a power series to approximate the definite integral, I, to six decimal places. x3...
(1 point) Find a power series centered at a = 0 for the function ln(1 +...
(1 point) Find a power series centered at a = 0 for the function ln(1 + x) When you have found the series, enter the sum of the first five non-zero terms of the series. Find the radius of convergence R of the power series. R= 1 Use the power series you found above, to build a power series for the function f(x) = x? ln(1 + x). Again, enter the first five non-zero terms. What is the radius of...
Find a power series representation for the function. (Give your power series representation centered at x...
Find a power series representation for the function. (Give your power series representation centered at x = 0.) Kx) = In(s - x) ) Ins) - (L ) Determine the radius of convergence, R. Find a power series representation for the function. f(x) = x2 tan-(x3) ax)= ] (! Determine the radius of convergence, R. R- Tutorial Exercise Evaluate the indefinite integral as a power series. What is the radius of convergence R? 11-12 de Step 1 Using Using ---...
Consider the function f(x) = e x a. Differentiate the Taylor series about 0 of f(x). b. ldentify ...
Please answer all, be explanatory but concise. Thanks.
Consider the function f(x) = e x a. Differentiate the Taylor series about 0 of f(x). b. ldentify the function represented by the differentiated series c. Give the interval of convergence of the power series for the derivative. Consider the differential equation y'(t) - 4y(t)- 8, y(0)4. a. Find a power series for the solution of the differential equation b. ldentify the function represented by the power series. Use a series to...
please do 9 Find a function f(x) with power series f(x) E-1n3 x" 9. 10. Use...
please do 9
Find a function f(x) with power series f(x) E-1n3 x" 9. 10. Use a power series to show that 0.999...= 1 n(1+1/n) 11. Determine the convergence/divergence of n-11+1/0 12. Find the length of the curve c(t) (Tt+e,2 cos t,2 sin t) for 0t T (1+3) converge? 13. To what value for the sequence an 14. Does the series ne- converge?V 15. Give an example of u, v E R3 perpendicular and with no zero entries in
Find...
15. Let f(x) = 2 . 2+x a) Find the power series representation of f(x) centered at o b) Use the power series representation to find ½ dx. 16. Find the Taylor Series for f(x) = sin (2x) centered a...
15. Let f(x) = 2 . 2+x a) Find the power series representation of f(x) centered at o b) Use the power series representation to find ½ dx. 16. Find the Taylor Series for f(x) = sin (2x) centered at T.
15. Let f(x) = 2 . 2+x a) Find the power series representation of f(x) centered at o b) Use the power series representation to find ½ dx. 16. Find the Taylor Series for f(x) = sin (2x) centered...
EXAMPLE 7 Find a power series representation for f(x) = arccot(x). SOLUTION We observe that f'(x)...
EXAMPLE 7 Find a power series representation for f(x) = arccot(x). SOLUTION We observe that f'(x) = -1/(1 + x2) and find the required series by integrating the power series for -1/(1 + x2). -1 arccot(x) = S — - dx (1 + x2) = S-1 - + x4 * + ...)dx = C - X+ To find C, we put x = 0 and obtain C = arccot(0) = n/2. Therefore = 1/2 - x + - + 00...
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...
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...
Find a power series representation for the function. f(x) = فيه (x – 4)2 00 f(x) = Σ no Determine the radius of convergence, R. R = Evaluate the indefinite integral as a power series. Je at c+ Σ ΦΟ η = Ο What is the radius of convergence R? R = Find the radius of convergence, R, of the series. 3n Σ n! n=1 R= Find the interval, 1, of convergence of the series. (Enter your answer using interval...
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Find a power series representation for the function. х f(x) (1 + 6x)2 f(x) = ( (-6).*- 1 nxt n = 0 x Determine the radius of convergence, R. R = 1/6 Evaluate the indefinite integral as a power series. t Vi dt 1 - 79 C+ Σ Σ( n = 0 What is the radius of convergence R? R= Use a power series to approximate the definite integral, I, to six decimal places. x3...
(1 point) Find a power series centered at a = 0 for the function ln(1 + x) When you have found the series, enter the sum of the first five non-zero terms of the series. Find the radius of convergence R of the power series. R= 1 Use the power series you found above, to build a power series for the function f(x) = x? ln(1 + x). Again, enter the first five non-zero terms. What is the radius of...
Find a power series representation for the function. (Give your power series representation centered at x = 0.) Kx) = In(s - x) ) Ins) - (L ) Determine the radius of convergence, R. Find a power series representation for the function. f(x) = x2 tan-(x3) ax)= ] (! Determine the radius of convergence, R. R- Tutorial Exercise Evaluate the indefinite integral as a power series. What is the radius of convergence R? 11-12 de Step 1 Using Using ---...
Please answer all, be explanatory but concise. Thanks.
Consider the function f(x) = e x a. Differentiate the Taylor series about 0 of f(x). b. ldentify the function represented by the differentiated series c. Give the interval of convergence of the power series for the derivative. Consider the differential equation y'(t) - 4y(t)- 8, y(0)4. a. Find a power series for the solution of the differential equation b. ldentify the function represented by the power series. Use a series to...
please do 9
Find a function f(x) with power series f(x) E-1n3 x" 9. 10. Use a power series to show that 0.999...= 1 n(1+1/n) 11. Determine the convergence/divergence of n-11+1/0 12. Find the length of the curve c(t) (Tt+e,2 cos t,2 sin t) for 0t T (1+3) converge? 13. To what value for the sequence an 14. Does the series ne- converge?V 15. Give an example of u, v E R3 perpendicular and with no zero entries in
Find...
15. Let f(x) = 2 . 2+x a) Find the power series representation of f(x) centered at o b) Use the power series representation to find ½ dx. 16. Find the Taylor Series for f(x) = sin (2x) centered at T.
15. Let f(x) = 2 . 2+x a) Find the power series representation of f(x) centered at o b) Use the power series representation to find ½ dx. 16. Find the Taylor Series for f(x) = sin (2x) centered...
EXAMPLE 7 Find a power series representation for f(x) = arccot(x). SOLUTION We observe that f'(x) = -1/(1 + x2) and find the required series by integrating the power series for -1/(1 + x2). -1 arccot(x) = S — - dx (1 + x2) = S-1 - + x4 * + ...)dx = C - X+ To find C, we put x = 0 and obtain C = arccot(0) = n/2. Therefore = 1/2 - x + - + 00...
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