Think about what this limit means: as the values of the independent varaiable increase without bound, the function values also increase without bound. It seems almost obvious that we should expect.
To complete that discussion it is necessary to consider the limits with > 0. Reciprocal powers were considered in the Limits at Infinity lesson. In many ways limits at infinity are the easiest to understand that is where the discussion begins. For one-sided limits values of are chosen from only one side of the the limit point. That is, for values of near, all of the function values must be increasing without bound. The underlying theme for each of these discussions is an infinite limit.
The lesson concludes with the definition of vertical and oblique asymptotes. Because these limit points are finite, it is necessary to consider both two-sided and one-sided limits. Functions that are not defined at points because of problems with division by zero are considered next. With this information it will be possible to evaluate all limits at infinity (or negative infinity) of rational polynomials - including those in which the degree of the numerator is larger than the degree of the denominator. The first goal is to complete our knowledge about limits at infinity for all power functions. This lesson continues some of the discussions begun in the Limits at Infinity lesson. Warning, the name changecoords has been redefined