Original
Compute:
{{MATH_97}}
{{CMD_98}}
Let's graph this function to see what's going on:
{{CMD_99}}
{{ENV_100}}
{{CMD_101}}
Remark: Since
{{MATH_102}}
it follows that
{{MATH_103}}
This remark is very important, since the function {{MATH_104}} has two factors:
{{CMD_105}}
{{ENV_106}}
{{CMD_107}}
Hence we have that when {{MATH_108}}
{{MATH_109}}
and we see
{{MATH_110}}
and so by the Squeeze theorem,
{{MATH_111}}
In a similar fashion, when {{MATH_112}},
{{MATH_113}}
and so
{{MATH_114}}
and again by the Squeeze Theorem {{MATH_115}}. Hence we see that
{{MATH_116}}
{{CMD_117}}
{{ENV_118}}
{{CMD_119}}
{{CMD_120}}
{{CMD_121}}