Answer the following question

Q5. (a) Let f(x, y) = V1+ x2 + y2. Find P2,(0,0) (x, y), the degree 2 Taylor polynomial of f at (0, 0). plot the graphs of the surfaces z = f(x, y) and z = P2, (0,0) (x, y) alongside one another. (b) Let g(x, y) = 2 + 5x + 6xy + y2. Find the degree 1 and degree 2 Taylor polynomials of g at (0, 0). What do you notice? (c) Now consider a function h that is a degree 2 polynomial in x and y, i.e., h(x, y) = A+ Bx + Cy+ Dx' + Exy + Fy, where A, B, C, D, E, F E R are constants. Make a conjecture about the degree 1 and degree 2 Taylor polynomials of h at (0, 0). (d) Prove your conjecture from part (c)