1. Consider the function f (x) =(from 0 to x) ? te^(?t^3) dt . Unfortunately, it

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1. Consider the function f (x) =(from 0 to x) ? te^(?t^3) dt . Unfortunately, it is not possible to write a formula for f any more explicitly than that since it would require computing a symbolic antiderivative of te^(?t^3) , which is impossible. (a) Show that near x=0, f(x)?A(x)=(x^2)/2 ?(x^5)/5 +(x^8)/16 ?(x^11)/66 (b) Estimate the error in this formula to calculate f(0.3) and f(0.5). Problem 2. Find the radius and interval of convergence for each of these series: (a) The MacLaurin series for ln(1+ x^2 ) . ? ? ???? ((2^n)(x?3)^n (b))/sqrt(n+3) ?n=0

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