Q4 (10 points) f(x) The notation f(x) ~ g(x) means that lim = 1. The x-cog(x) purpose of this question is to show that X dt ~ In(t) In(x) (a) (4 points) Determine whether the improper integral dx In(x) converges. Explain your reasoning. (Hint: look at the tangent line of In(x) at x = 1.) (b) (6 points) Deduce the relation X dt ~ In(t) In(x) (Hint: You may want to use I'Hopital's rule.)