Find the Maclaurin series for sin x and prove that it representssin x for all x ? R.(ii) Deduce the power series expansion (centered at 0) for cos x,for every x ? R.(iii) Find the first three nonzero terms in the power seriesrepresentation (centered at 0)for tan x.(iv) Use Part (iii) to evaluate

Solve Using Calc 2

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lim x →0 tan x - x x3 lim x →0 tan x - x x3