The Linearization of the function f(x,y) at the point (a,b), also called the first-degree Taylor Polynomial of fat (a,b), is given by: L(x, y) = f (a, b) + fx(a, b)(x - a) + fy(a,b) (y -b) Find the first-degree Taylor Polynomial of f(x,y) = xe at the point (1,0). Show that f and L share the same first derivatives at (1,0). How do the two functions compare near (1,0)? The Quadratic Approximation of the function f(x,y) at the point (a,b), also called the second-degree Taylor Polynomial of fat (a,b), is given by: Q(x, y) = f(a, b) + fx(a,b)(x - a) + fy(a,b)(y -b) +, fux (a, b)(x - a)' + fry (a, b)(x - a )(y - b) + ; fry(a, b)(y -b)= Find the second-degree Taylor Polynomial of f(x,y) = xe at the point (1,0). Show that f and Q share the same first and second derivatives at (1,0). How do the two functions compare near (1,0)? How many terms would be required to construct the third-degree Taylor Polynomial? (Hint: How many terms are there in a Taylor Polynomial of zeroth-degree?)