$($b$)$

$\underset{n}{lim}\frac{(2n)!\sqrt[\phantom{2}]{n}}{(n!{)}^2{4}^n}$

$($c$)$

${\displaystyle \underset{-}{\overset{}{}}}$dxcos$(x)(\frac{}{4}-x^2)$

$($d$)$

${\displaystyle \underset{0}{\overset{1}{}}}d{?}^2(1-x^2{)}^{\frac{5}{2}}$