Hello, please see the attached picture and answer the problems shown below. Please ensure that every problem is correct, show your detailed work, and write legibly!! :) Thank you so much and if you have any questions, don't hesitate to ask!!! Please, underneath each, explain how you went about doing the problem!!

1 : Evaluate the following limits. lim xy - x a) (x,y)-(0,0) 24 + 94 3 - 4x2y + 3xy2 - 12y3 b) lim (z,y) - (4,1) x2 - xy - 12y2 C) lim sin x (cosy - 1) (x,y)->(0,0) In(y + 1) tan lx 2 : Let f(x, y) = - y . Find x+1 Ox using the definition of partial derivatives. No credit if you do not use the definition. 3 : Let f(x, y) = 4x3y2 - 2xy2 -x + 1. Find the approximate value of f (1.003, 2.001) using total change and partial derivatives