$($a$)$ Let $$ and $$ be positive constants. Find

$\underset{x{0}^{+}}{lim}\frac{1-(1+x^{}{)}^{-}}{x}$

$($b$)$ It is estimated that t years from now the populatic of a certain town will be

$F(t)=40-\frac{8}{t+2}$ million

Use differentials to estimate the amount by whi population will increase during the next $6$ months