MinLimit
MinLimit[f, x -> x*] gives the min limit as x approaches x*.
MinLimit[f, {x1 -> x1*, ..., xn -> xn*}]gives the nested min limit.MinLimit[f, {x1, ..., xn} -> {x1*, ..., xn*}]gives the multivariate min limit.
Examples
MinLimit[Sin[x]/x, x -> 0]MinLimit[x^2 + y, {x -> 0, y -> 1}]Please visit the official Wolfram Language Reference for more details.