Original
Compute
{{MATH_123}}
{{CMD_124}}
This doesn't appear to be suitable for L'H{{CMD_125}}pital's Rule. As {{MATH_126}}
approaches zero, {{MATH_127}} goes to {{MATH_128}}, so the product looks like
{{MATH_129}}
This product could be anything. A careful analysis is required.
Write
{{MATH_130}}
Set {{MATH_131}} and {{MATH_132}}. Since both functions are differentiable near zero and
{{MATH_133}}
we may apply L'H{{CMD_134}}pital's rule. Write with me
{{MATH_135}}
and
{{MATH_136}}
so
{{ENV_137}}
One way to interpret this is that since {{MATH_138}},
the function {{MATH_139}} approaches zero much faster than {{MATH_140}} approaches
{{MATH_141}}.
{{CMD_142}}
{{CMD_143}}