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In Problems 724, find a power series converging to f(x) and determine the radius of convergence. 25 Find the Taylor series for ln x in powers of x  1. 26 Find the Taylor series for sin x in powers of x  π/4. 27 Use Taylor's Formula to prove that the binomial series converges to (1 + x)^{p} when ½ ≤ x < 1. (The proof in the text shows that it actually converges to (1 + x)^{p} for  1 < x < 1.) 28 Let f(x) = 0 if x = 0, f(x) = e^{1/x²} if x ≠ 0, Show that f^{(n)}(0) = 0 for all integers n; so for x ≠ 0 the MacLaurin series converges but to zero instead of to f(x).


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