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Let g : R' - R be defined as g(x, y) = In(ax2 + by- + 1) with a > b > 0. (a) Find P2,(0,0) (x, y), the degree 2 Taylor polynomial of g at (0, 0). Show all your work. (b) Prove that there exits a constant M > 0, such that In(ax2 + by- + 1) M - 1 5 ax2 + by2 bVx 2+ 2 (c) Using part (b), evaluate lim c In(ax2 +by2+1) , with c * 0. (x, y)-(0,0) ax2 + by2