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(1) Let f() = 3 (i) Show that f(x) = -3. and then use the geometric sum formula to expand f (x) into a series centered at a = 0. (ii) Use the Taylor formula for coefficients on to obtain a series for f(a). (iii) Show that both sums obtained in (i) and (ii) are identical. (2) Expand f(x) = cos x into a Taylor series centered at the origin (a = 0). (3) Compute an approximation of f(x) = tan x by computing the coefficients Co, C1, C2, C3 (a = 0). Then graph y = tan x and the obtained cubic polynomial in the same coordinate system. As you zoom on the origin (0, 0) do these two graphs get closer? (4) By computing coefficients on with center a = 0 establish that In(x + 1) = 2 -2 + .. CO (5) Find the first 5 terms (a quartic polynomial) of the Taylor series for f (x) = 10*