= (1 point) The Taylor series for f(x) = cos(x) at a = Σc(x. À is cr(x - 5)". TT 4 n=0 Find the first few coefficients.

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= (1 point) The Taylor series for f(x) = cos(x) at a = Σc(x. À is cr(x - 5)". TT 4 n=0 Find the first few coefficients. Co = C1 = C2 = C3 = = C4 =

8 + 3x (1 point) Let f(x) = х Compute = = = f(x) f'(x) f"(x) f"(x) = f(iv)(x) = f(u)(x) = ) = = We see that the first term does not fit a pattern, but we also see that f(k)(1) = for k > 1. Hence we see that the Taylor series for f centered at 1 is given by f(x) = 11 + Σ (x - 1)k. k=1

= (1 point) Write the Taylor series for f(x) = x3 about x = 3 as c„(x – 3)". 00 n=0 Find the first five coefficients. Co= Ci= C2= C3= C4=

= 00 (1 point) The function f(x) = 9x2 arctan(x3) is represented as a power series f(x) = { c,x". Σ ” n=0 What is the lowest term with a nonzero coefficient. n= Find the radius of convergence R of the series. R=

(1 point) Write the Maclaurin series for f(x) = 5x2e-8x as c»x". n=0 Find the first six coefficients. Co= Ci= C2= C3= C4= C5=