Original
Compute:
{{MATH_51}}
{{CMD_52}}
To find the form, notice that {{MATH_53}} and {{MATH_54}}. This means
our limit has the form {{CMD_55}}.
However, note that if we assume {{MATH_56}}, then we can write
{{MATH_57}}
{{CMD_58}}
{{ENV_59}}
{{CMD_60}}
{{ENV_61}}
{{CMD_62}}
So, ``our function" is equal to the polynomial {{MATH_63}} everywhere, except at {{MATH_64}}. Therefore, for all values of {{MATH_65}} near {{MATH_66}}, ``our function" is equal to the polynomial {{MATH_67}}!
This means that
{{MATH_68}}
But now, we have to take the limit of a polynomial,
{{MATH_69}}.
Hence
{{MATH_70}}
{{CMD_71}}
{{CMD_72}}