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- Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = x 16 + x2 f(x) = ∞ n = 0 Determine the interval of convergence. (Enter your answer using interval notation.)arrow_forwardFind a power series representation for the function. (Center your power series representation at x = 0.) Determine the interval of convergence. (Enter your answer using interval notation.)arrow_forwardUsing the Taylor's formula (not the formula for ln(x)).find the Taylor series centered at 1 for f(x) = ln(x) . Show at least the first four non-zero terms and then write it in summation notationarrow_forward
- find a power series representation for the function. determine the interval do convergence. (give your power series representation centered at x=0). f(x) = x/(3x^(2)+1).arrow_forwardFind a power series representation for the function. Determine the interval of convergence. f(x) = 1/(6+x)arrow_forwardFind the radius of convergence and the interval of convergence of the series. Test the endpoints. [summation symbol from n=1 to infinity] (x-3)n/3nn!arrow_forward
- Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x)=x/13x^2+1 Determine the interval of convergence. (Enter your answer using interval notation.) Need help finding interval of convergencearrow_forwardusing integral test decide if the series converges or diverges show all stepsarrow_forwardProve that the series diverges at x = 3 (Limit Comparison Test) Prove that the series converges at x = 11 (Alternating Series Test) Find the radius and interval of convergence of the series.arrow_forward
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