 In this video, we present the solution to question number four from practice exam number two from math 12 10 In which case we're asked to compute the limit as x approaches infinity of the rational function x plus x to the seventh over 10 x squared minus x to the seventh as we are looking for the limit as x approaches infinity of a rational expression We can focus just on the dominant term on top and bottom with the fastest Growing term as we go towards infinity for which a rational function We just you know given these polynomials we look for the leading term. We're gonna get an x to the seventh on the top We get a negative x to the seventh on the bottom So the limit as x approaches infinity here will be identical to just taking x to the seventh over negative x to seventh We only need the leading terms Those are the most dominant in terms of growth as x goes towards infinity in which case then we can simplify that just To be the limit of negative one as x approaches infinity, which is a constant so we get negative one here We recognize that this rational function is in fact a balanced rational function So the limit as x approaches infinity would just be The ratio of the leading coefficients one divided by negative one and so we see that the correct answer is a