Prove that if X[n]->L, X[n] doesn't equal 0 for all n, L doesn't equal 0 and Y[n]->M, then (Y[n]/X[n])->(M/L).
They only give you the squeeze theroem and that if X[n] converges then it's limit is unique. O and the definition. A sequence of reals has limit L iff for every epsilon>0 there exists a natural number N such that if n>N, then |X[n]-L|<epsilon
The Attempt at a Solution
The problem lies in I don't even know where to begin. I know to suppose the antecendent and i think that i let epsilon>0 and choose N belonging to the set of Naturals such that N is greater then some number but I have no idea what it would be. Usually in the examples and previous problems it would be something like, for some real number C, C*epsilon but I don't see a strategy like that taking me anywhere.