If$$x$2+$x$+1$f$($x$)$x$+2$for$$all$$x$,$find$$limx$1$f$($x$).$If$$x$2+$x$+1$f$($x$)$x$+2$for$$all$$x$,$find$$limx$1$f$($x$).$

Enter only the value of the limit in the space provided below. If the answer is not an integer, enter it as a fraction in simplest form. Do not enter a mixed number. If the limit does not exist, enter $$does not exist$.$