3-12 Find a power series representation for the function and determine the interval of convergence. 1 X 3. f(x) = 4. f(x) = 1 + x 1 + x 1 5 5. f(x) 6. f(x) 1 x² 1 - 4x² =
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- (a) Find a power series representation for the function.f(x)=2/(19+x) (b) Determine the interval of convergence.(a) Find a power series representation for the function.f(x)=x**3/(x-11)**2 (b) Determine the radius of convergence.R =6. Consider xn+1 = (1/3)(2xn - 9/xn2). Does it converge for any nonzero initial point? If so, to what values?
- infinity sigma k=0 (-1)^k(k+1)x^k. Use that result to create a power series representation of f(x) = x/(1+x^4)^2Sigma k=1 to infinity -20*8^k/4*9^k series converges or diverges. show stepsVv Express the function f(x) = a ln(1+cx) in power series form. Then evaluate the series at x = 0.127 using the first five terms of the series if a = 15.6 and c = 2.
- For the given function: g(x)= x/2x^2 +1 1. Find a power series representation. 2. Write the first four terms of the series. 3. Determine the interval of convergence.Use the power series method to solve the given initial-value problem. (Enter the first four nonzero terms.) (x + 1)y'' − (2 − x)y' + y = 0, y(0) = 8, y'(0) = −1 y =(x+1)y''-(2-x)y'+y=0 y(0)=2, y'(0)=-1 What are the first six non zero terms of the power series?
- decide if the given statement is true or false,and give a brief justification for your answer.If true, you can quote a relevant definition or theorem .If false,provide an example,illustration,or brief explanation of why the statement is false.Q.)` The radius of convergence of a power series solution to the differential equation y′′+ 1/x2−1 y′+ 1/x +2 y =0 centered at x =2 is at least 2.8.6.26. Find a power series representation of f(x) about c = 0 (refer to example 6.6). Also, determine the radius and interval of convergence, and graph f(x) together with the partial sums and .Find a power series solution of the differential equation given below. Determine the radius of convergence of the resulting series, and use the series given below to identify the series in terms of familiar elementary functions.