Determine \[ \lim_{x\to 2}\frac{x^2+2x-24}{x-2}. \]

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Lesson Parent: 
Function Limits V: Properties of Function Limits
Problem: 

Determine
\[
\lim_{x\to 2}\frac{x^2+2x-24}{x-2}.
\]

Answer: 

The limit does not exist.

SAMPLE SOLUTION

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Solution: 

Usually when <Sign in to see all the formulas> and <Sign in to see all the formulas> the limit <Sign in to see all the formulas> does not exist. However, if we can find an $x-2$ in the numerator to cancel the $x-2$ in the denominator then the function limit might exist.

We know that

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Unfortunately, there is no $x-2$ in the numerator so this function limit does not exist.