Original
Using the Composition Limit Law, we can compute the last example from the beginning of this section.
{{CMD_241}}
Compute the following limit using limit laws:
{{MATH_242}}
{{CMD_243}}
We will use the Composition Limit Law.
Let
{{MATH_244}}
where {{MATH_245}}, and {{MATH_246}}.
Now, continuity of {{MATH_247}} implies that {{MATH_248}}.
Continuity of {{MATH_249}} implies that {{MATH_250}} is continuous at {{MATH_251}}.
Now, the Composition Limit Law implies that
{{MATH_252}}
{{CMD_253}}
We can confirm our results by checking out the graph of {{MATH_254}}:
{{MATH_255}}
{{CMD_256}}
{{CMD_257}}
{{CMD_258}}