When do you rationalize the denominator to calculate the limit?
At the risk of sounding like I'm being flippant, you rationalize the denominator when you need to and it helps.
Example 1: Evaluate:
The limits of the numerator and denominator are:
Example 2: Evaluate:
This time the limits of the numerator and denominator are
We cannot use the quotient rule for limits, so we'll try rationalizing the denominator to see if that helps.
(Yes, really, seriously. Try something and see if it works. There is no 'cookbook'. for solving all problems.)
The denominator of this new ratio does not go to
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