$(b)$ Find a degree $2$ Maclaurin polynomial for the function $f(x)=1+x{e}^{1-x}.$

$(c)$ Determine $(if$ they exist$)$ the following $limits$

$a\underset{x0}{lim}\frac{e^{x^2}-1}{xcos(x)+sin(-x)}$

$b\underset{x1}{lim}\frac{e^{x-1}-1}{x^2-1}.$