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- Find two linearly independent power series solutions centered at x0=0 to y''+x2y = 0 state the interval of convergence for these power series.A) obtain the power series representation for 1/1-x^2 = sigma k=0 to infinity B) what is the interval of convergenceFind a power series representation for the function. f(x) = x (1 + 7x)2 Then determine the radius of convergence
- Find a power series representation for the function of convergence. f(x) = 1/1+4x^2 and determine the radius.Find the Taylor series for f(x) = ln(x+1) at x = 0. What is its radius of convergence?Find the radius of convergence R of the power seriesΣ∞ n=1 (x − 3)n 4n n. Then find itsinterval of convergence
- Find the taylor series at x=0 for the function f(x)= 1/(1-2x). Then find the radius of convergence.(a) Find a power series representation for the function.f(x)=2/(19+x) (b) Determine the interval of convergence.Use the power series 1/(1+X)= ∑_(n=0)^∞▒(-1)^n x^(n^ )to determine a power series at 0, for the function f(x) and identify the interval of convergence.f(x)=2/(x+1)^3 = d^2/(dx^2 ) [1/(x+1)] Also, see the attached picture of the problem, it is better. Thank you.