QUESTION $3$

For $a,b>0$ and $z=\sqrt[\phantom{2}]{4-a{x}^2-b{y}^2},$ the approximate change as $(x,y)$ moves from $(1,1)$ to $(1\mathrm{.}01,0\mathrm{.}99)$ is given by:

a$.\frac{-(0\mathrm{.}01)(a-b)}{2\sqrt[\phantom{2}]{4-a-b}}$

b$.\frac{(0\mathrm{.}01)(a-b)}{2\sqrt[\phantom{2}]{4-a-b}}$

c$.\frac{-(0\mathrm{.}01)(a-b)}{\sqrt[\phantom{2}]{4-a-b}}$

d$.\frac{2(0\mathrm{.}01)(a-b)}{2\sqrt[\phantom{2}]{4-a-b}}$

$\frac{2(0\mathrm{.}01)(a-b)}{\sqrt[\phantom{2}]{4-a-b}}$