Question

Raju wants to obtain a quadratic surface close to the surface z = e ^ (xy) . Obtain an equation of the required quadratic surface and the general error function in this approximation. What is the equation of the linear approximation to this quadratic surface? Is it the same as that of the surface z = e ^ (xy) ?​

Answer 1

Answer:

The Quadratic Approximation to a function z=f(x,y) at (a,b) is given by

The Quadratic Approximation to a function z=f(x,y) at (a,b) is given byQ(x,y) = f(a,b)+fx∣∣(a,b)(x−a)+fy∣∣(a,b)(y−b)

The Quadratic Approximation to a function z=f(x,y) at (a,b) is given byQ(x,y) = f(a,b)+fx∣∣(a,b)(x−a)+fy∣∣(a,b)(y−b)+12fxx∣∣(a,b)(x−a)2+fxy∣∣(a,b)(x−a)(y−b)+12fyy∣∣(a,b)(y−b)2.

The Quadratic Approximation to a function z=f(x,y) at (a,b) is given byQ(x,y) = f(a,b)+fx∣∣(a,b)(x−a)+fy∣∣(a,b)(y−b)+12fxx∣∣(a,b)(x−a)2+fxy∣∣(a,b)(x−a)(y−b)+12fyy∣∣(a,b)(y−b)2.At (x,y)=(a,b), the value, first derivatives and second derivatives of Q(x,y) equal the value, first derivatives and second derivatives of f(x,y). In fact, Q(x,y) is the unique quadratic polynomial with this property.

Step-by-step explanation:

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