Question: Question deals with Quadratic Approximation in Vector Calculus (2) Consider the function f: R4 e R3 given by f($3y1z3w):(1 + x i 2y i '92,

Question deals with Quadratic Approximation in Vector Calculus

(2) Consider the function f: R4 e R3 given by f($3y1z3w):(1 + x i 2y i \"'92, 39.271\": 2ySm(w + 1132)). (a) Find the quadratic approximation Jgf of f at the point P = (0, 0, 0, 0). (b) Now consider the function g : R3 e R2 given by g(:c,y,z) = (311101: f y): yCOS(.'I:2 i 32 i 1))' We can compose the maps f and g to obtain a smooth function g 0 f : R.4 > R2. Use the chain rule to compute Dp(g o f), where P : (0,0, 0,0)

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