Final answer:
The linearization of f(x,y)=ln(1+x+y) at (0,0) is L(x,y) = x + y.
Step-by-step explanation:
To find the linearization of the function f(x, y) = ln(1+x+y) at the point (0,0), we will use the formula for the linearization:
L(x,y) = f(0,0) + fx(0,0)(x-0) + fy(0,0)(y-0)
Where fx(0,0) and fy(0,0) are the partial derivatives of f with respect to x and y, evaluated at the point (0,0). In this case, fx(0,0) = 1 and fy(0,0) = 1, so the linearization becomes:
L(x,y) = ln(1) + (1)(x-0) + (1)(y-0) = x + y