a) $$x=\frac{1+y}{1+2z^2}$$ b) $$ \lim_{x\to 0}{\frac{e^x-1}{2x}} \overset{\left[\frac{0}{0}\right]}{\underset{\mathrm{H}}{=}} \lim_{x\to 0}{\frac{e^x}{2}}={\frac{1}{2}} $$ c) $$F(x,y)=0 ~~\mbox{and}~~\left| \begin{array}{ccc} F”_{xx} F”_{xy} & F’_x \\ F”_{yx} & F”_{yy} & F’_y \\ F’_x & F’_y & 0 \end{array}\right| = 0$$ d) $$\int_0^\infty e^{-x^2} dx=\frac{\sqrt{\pi}}{2}$$