Solving limits with factoring
When substitution doesn’t solve the limit, try factoring
When you can’t just plug in the value you’re evaluating, your next approach should be factoring.
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Factor the function to cancel any removable discontinuities, then evaluate the limit
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How to evaluate a limit using factoring and cancellation
Example
Evaluate the limit.
???\lim_{x\to 4}\frac{x^2-16}{x-4}???
Just plugging in ???4??? would give us a nasty ???0/0??? result. Therefore, we’ll try factoring instead.
???\lim_{x\to 4}\frac{(x+4)(x-4)}{x-4}???
When you can’t just plug in the value you’re evaluating, your next approach should be factoring.
Canceling ???(x-4)??? from the top and bottom of the fraction leaves us with something that is much easier to evaluate:
???\lim_{x\to 4}x+4???
Now the problem is simple enough that we can use substitution to find the limit.
???4+4???
???8???
