Hi!
Any help?
Q:
Determine the quadratic approximation surface at the point (0,0) on the surface of
z=sqrt(x+1)/(y+1)
Start by defining the "quadratic surface" by the standard form and we'll find values for the coefficients such that . Since this is a system of six equations and six unknowns, we are guaranteed a unique answer.
Derivatives of z:
Derivatives of q:
So, is a quadratic function that shares its six derivatives with . Notice that this is always possible, as long as all six derivatives exist and are defined at the point of interest.