Show that $\backslash$lim$\_($x$->\backslash$infty $)($x$^($n$))/($e$^($x$))=0$ for any positive integer n$.$

Find the value$($s$)$ of of the constant k which make f$($x$)=\{(($sinx$-1)/($x$-(\backslash$pi $)/(2))$ if x$!=(\backslash$pi $)/(2)),($k if x$=(\backslash$pi $)/(2))$:$\}$

continuous at x$=(\backslash$pi $)/(2).$

Find all values of k and m such that $\backslash$lim$\_($x$->1)($k$+$mlnx$)/($x$-1)=5$