Given the function g$($x$)=$e$2$x$,$ which of the following is the correct limit definition of g$($a$)?$

Select the correct answer below:

limh$0$e$2$h$$e$2$ah

limh$0$e$2$a$+$h$$e$2$ah

limh$0$e$2$a$+$h$$e$2$hh

limh$0$e$2($a$+$h$)$e$2$ah