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- find power series expansion of the functionFind Taylor series for function f(x) =lnx centered at a=1Use the zero-to-three Taylor series expansion to predict f(2,5) for f(x)= ln x using base point x = 1. Calculate the true relative error for each approximation. Note: The derivative of ln(g(x)) = (1/ g(x)) . g’(x)
- Find the power series representation of ln[1 + x] either by differentiation orintegration of the power series or by finding p(x), the Taylor series. Determinethe interval of convergence.Use power series operations to find the Taylor series at x = 0 for thefunctions 1/(1 - x)2determine the Taylor series about the point x0 for the given function. Also determine the radius of convergence of the series. 7.sinx,x0=0
- Use power series operations to find the Taylor series at x = 0 for thefunctions cos2 x2. Find the Taylor Series representation of f(x) = sin 3x centered at x = pi/2 using the definition. idk what do next?pls provide detailed solution using divergence and p-series find out if the ff. series diverge or converge: