To prove that you divide both sides by x and take the limit for x -> inf, applying L'Hopital rule the limit is zero, so there is such a C, any number greater th

To prove that you divide both sides by x and take the limit for x -> inf, applying L'Hopital rule the limit is zero, so there is such a C, any number greater than zero. The existence of such X is just the definition of limit when x tends to inf. Another way, just using a cas (like maxima) to compute such limit: (%i1) limit( (log(x^2 + 1) + sqrt(x) + x/exp(sqrt(4*x + 3)))/x,x,inf); the result is zero.