In the previous example, we used the fact that {{MATH_75}} when {{MATH_76}} is negative. If the limit were as {{MATH_77}}, then {{MATH_78}} and {{MATH_79}} would each eventually be positive valued. This would have made {{MATH_80}}. Repeat the calculation from the previous example, finding the limit {{MATH_81}} taking note to use {{MATH_82}} in your simplification. You'll find that the two limits (as {{MATH_83}} and as {{MATH_84}}) have different values.