Some questions from old exams??

1)

a) $\displaystyle \lim_{(x,y)\rightarrow(0,0)}\frac{sin(xy)}{x}$

b) $\displaystyle \lim_{(x,y)\rightarrow(0,0)}\frac{xy^2}{x^4y^4}$

2) Without using distance formula, find the distance from the point (0,1,1) to the plane $\displaystyle 4y+3z=-12$

3) A closed box to be found to have length 2ft, witdh 4ft and hight 3ft, where the measurement of each dimension ismade with a maximum possible error of +-0.02ft. The top of the box is made from material that costs only 1.50 Dollars/$\displaystyle ft^2$. What is the maximum error involved in the computation of the cost of the box?

4) Find an equation for the tangent plane to the surface $\displaystyle z=e^{-(x^2+y^2)}$ at (0,0,1).

5) A right circular cone is measured and is found to have base radius r=40cm and altitude h=20cm. If it is known that each measurement is accurate to within %2, what is the maximum percentage error in the measurement of the volume?

These are five of the problems which i couldn't solve. i'll try others based on answers of these.

Any help is appriciated. =)