Limit calculation from the very definition

See Adam Strzebonski: Mathematica Journal 7:4(2000).

<<  Developer`;  <<  
      Experimental`;

Resolve[
        ForAll[ϵ, ϵ > 0, 
          Exists[M,  M  ∈ Reals,  
            ForAll[x,  
              x  > M &&  
                a ∈  
                  Reals,  -ϵ  <  ((3  (x^2) - 5  x + 7)/(7  (x^2) - 2  x + 11)) - a < ϵ]]], {a}] // Timing