Use$$the$$Squeeze$$Theorem$$to$$find$$limx$1|$x$1|$sin$2$x$+1.$Use$$the$$Squeeze$$Theorem$$to$$find$$lim$1|1|$sin$2+1.$

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$.$