III. A non-polynomial definite integral So far we have only used the definition of the definite integral to compute integrals of polynomials. In fact we have had to restrict ourselves to polynomials of degree no more than three. We will now endeavor to find ex dx o For this we will need a new summation formula. Hopefully you are all familiar with geometric sequences and their sums from algebra. For ease in this exercise we will use the following version of the summation formula ark-1 _ a(1 -rn) 1-r K =1 Before we move on to the integral above it will be helpful to review some of our limit skills from first quarter calculus that will be needed to evaluate the integral. 7) Find lim x(1 - e /x). Show all your work. x-+00 (Hint: this is an indeterminate form.) (10 points) Now we have all the tools to evaluate our definite integral. This time it would serve you well if you use the left hand endpoints in your Riemann sum. 8) Evaluate [ ex dx. Show all your work. (10 points)