(3) The goal of this problem is to approximate √ 1.0101. (a) What function f(x, y) gives √ XXXXXXXXXXwhen evaluated at (.1, .01). At what nearby point (x0, y0) can one reasonably compute the value of...

(3) The goal of this problem is to approximate √ 1.0101.

(a) What function f(x, y) gives √ 1.0101 when evaluated at (.1, .01). At what nearby point (x0, y0) can one reasonably compute the value of f(x0, y0) without using a calculator.

(b) Find the tangent plane p1(x, y) of f(x, y) from part (a) at the point (x0, y0).

(c) Find the second order Taylor approximation p2(x, y) of f(x, y) from part (a) at the point (x0, y0).

(d) Evaluate p1(.1, .01) and p2(.1, .01) by hand. Using a calculator, the first five decimal places of √ 1.0101 is 1.00504. Which gave a better approximation p1 or p2?