Question 2 Let z = 2y - ln(2x + y). Find the second order Taylor polynomial at x = 0 and y = 1 and use it to estimate z(.3, 1.2).

Show each derivative step in generating the fourth order Taylor polynomial for ln(x) centered at one. Do not approximate.

2. Find the polynomial interpolation of y = cos a close to the point x = 0 by (a) Evaluating the function at the points (ro, 21, 2) = (-1,0,1). (b) Evaluating the function at the points (ro, 1,2)=(-4,0, 4). (c) Finding the second-degree Taylor polynomial around to = 0. (d) What do you think the interpolating polynomial would look like if y = cos z was evaluated at the points (To, 1, ₂) = (-a, 0, a) with a 0?

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