Question deals with Quadratic approximations in vector calculus. The instructor never went over this type of question.

(2) Consider the function f : R4 R3 given by 2 yzw , 2ysin(w + x2)). y, z, w) = (1 zy wy , e (a) Find the quadratic approximation JB f of f at the point P (0, 0, 0, 0). (b) Now consider the function g : R 3 + R2 given by (sin@ We can compose the maps f and g to obtain a smooth function g o f : R y), ycos@2 2 + R2. Use the chain rule to compute Dp(g o f), where P (2) Consider the function f : R4 R3 given by 2 yzw , 2ysin(w + x2)). y, z, w) = (1 zy wy , e (a) Find the quadratic approximation JB f of f at the point P (0, 0, 0, 0). (b) Now consider the function g : R 3 + R2 given by (sin@ We can compose the maps f and g to obtain a smooth function g o f : R y), ycos@2 2 + R2. Use the chain rule to compute Dp(g o f), where P