Please provide the answer with a detailed explanation.

Show your work. There should be either computations, or explanations of your steps or both. Do not provide only the final answer. 1. Compute the limit or show that the limit does not exists (a) lim (x,y)-(0,0) xy * 2 + 8 2 + 1 (b) lim (x,y)-(0,0) _xx (c) lim (xy)-(0,0) x cos(y) 2. Let f(x,y)=x3 +2x2y+y2.Compute (a) fx (b ) fy (c) fxx (d) fxy (e) fyy (f) fxxy 3. Find the equation of the tangent plane to the surface z = x2 + 2xy + y at the point (1, 2). 4. Find the linear approximation of f(x,y)=x2+2xy+y at the point(1,2). 5. Let z = x2 + 2xy + y2. Express dz in terms of dx and dy