I. Let f : R2 → R be defined by f(x)l cos (122) 211 Compute the second order Taylor polynomial of f near the point xo - 0. A Road Map to Glory (On your way to glory, please keep in mind that f is class C) a) Fill in the blanks: The second order Taylor's polynomial at h E R2 is given by T2 (h) = 2! b) Compute the numbers, vectors and matrices that went into the blanks above. c) Use the formulation of the remainder term of the Taylor expansion to prove directly that lim 11-0 11시 2 Hint: Recall, that . The third derivative is a continuous map D3f (xo) : R2 → L (R2.L (R2,R)) and is therefore bounded on B (0, ll 1) For any cE B (0, h, D3 f (c) is trilinear map and D3f (c) (h, h, h)D3f ( lhll I. Let f : R2 → R be defined by f(x)l cos (122) 211 Compute the second order Taylor polynomial of f near the point xo - 0. A Road Map to Glory (On your way to glory, please keep in mind that f is class C) a) Fill in the blanks: The second order Taylor's polynomial at h E R2 is given by T2 (h) = 2! b) Compute the numbers, vectors and matrices that went into the blanks above. c) Use the formulation of the remainder term of the Taylor expansion to prove directly that lim 11-0 11시 2 Hint: Recall, that . The third derivative is a continuous map D3f (xo) : R2 → L (R2.L (R2,R)) and is therefore bounded on B (0, ll 1) For any cE B (0, h, D3 f (c) is trilinear map and D3f (c) (h, h, h)D3f ( lhll