1. The problem statement: greek letters used here: xi, eta The Mean Value theorem applied to f(x,y) = sin(x^2 + y^2) implies with a = 0 and b = 0. sin(x^2 + y^2) = 2 xi cos( xi^2 + eta^2)x + 2 eta cos(xi^2 +eta^2) y find xi and eta or an accurate approximation to them as a function of x and y. 2. What i have tried doing: Let f(x,y) and its first order partial derivatives be continuos in an open region R and let (a,b) and (x,y) be points in R such that the straight line joining these points lies entirely within R. Then there exists a point (xi, eta) on that line between the endpoints. So we get f(x,y) = f (a,b) + f_x (xi, eta) (x-a) + f_y (xi,eta) (y-b) ** I am not sure where to go ahead from here, I would just like an idea as to what i can do to find the answer i dont want anyone to solve it as i would love to solve it but i just want someone to shed some light for me to go in the right direction. THANX for all the help.