7. Which of the following inequalities are correct?\\
(a) $1 + x \leq e ^ { x }$ for all $x \in \mathbb { R }$\\
(b) $2 ^ { n } \leq 2 n$ ! for all positive integers $n$\\
(c) $\left( 1 + x ^ { 2 } \right) ^ { n } \leq ( 1 + x ) ^ { 2 n }$ for all $x \in ( 0 , \infty )$\\
(d) $\sin ( x ) \leq \tan ( x )$ for all $x \in \left( - \frac { \pi } { 2 } , \frac { \pi } { 2 } \right)$\\