Consider the surface of the form z = f (x, y), which can be written as z - f(x, y) = 0.
a. Find a general equation for the tangent plane of the surface at the point P = (x0, y0, f(x0, y0)).
b. Solve the equation in part a, as an equation of the form P = L(x, y), The function L(x, y) is called a linear approximation of the surface at the point P.
c. Let f (x, y) = x cos (xy) - y sin (xy) and P = (1, 0, 1).
Use the results from parts a and b to find an estimate for the value of f (1.01, -0.1).
d. What is the true value of f (1.01, -0.1), what is the error in your approximation?