` lim_( x to infty) ((x+6)/(x+1))^(x+4) `= …… .

Answer

`e^(5)`

Explanation

`underset( x to infty) lim ( ( x+ 6)/( x + 1))^(x+4) = underset( x to infty) lim ( 1 + 5/( x + 1))^( x+ 4) " " [ 1^(infty) " form"]`
` = e^(underset( x to infty) lim (5(x + 4))/(x + 1)) = e^(5)`