Find the polynomial P1(x) = a0 + a1x whose value and slope agree with the value and slope of f(x) = cos x at the point x = 0. (a) Find the polynomial P2(x) = a0 + a1x + a2 x2 whose value and first two derivatives agree with the value and first two derivatives of f(x) = cos x at the point x = 0. This polynomial is called the second-degree Taylor polynomial of f(x) = cos x at x = 0. (b) Complete the table comparing the values of f(x) = cos x and P2(x). What do you observe? d) Find the third-degree Taylor polynomial of f(x) = sin x at x = 0.
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