Compute: {{MATH_148}} {{CMD_149}} We've already considered part of this example, but now we consider the two-sided limit. We already know that {{MATH_150}} and that this limit is of the form {{CMD_151}}. We also know that as {{MATH_152}} approaches {{MATH_153}} from the right, {{CMD_154}} {{CMD_155}} The numerator is a negative number. {{CMD_156}} The denominator is positive and approaching zero. {{CMD_157}} Hence our function is approaching {{MATH_158}} from the right. As {{MATH_159}} approaches {{MATH_160}} from the left, {{CMD_161}} {{CMD_162}} The numerator is negative. {{CMD_163}} The denominator is negative and approaching zero. {{CMD_164}} Hence our function is approaching {{MATH_165}} from the left. This means {{MATH_166}} {{CMD_167}} We can confirm our results of the previous two examples by looking at the graph of {{MATH_168}}: {{MATH_169}} {{CMD_170}} {{CMD_171}} {{CMD_172}}