Arturo O. answered • 05/18/18

Experienced Physics Teacher for Physics Tutoring

^{5}- a

^{5})/(x

^{2}- a

^{2})

Arturo O.

05/18/18

Prateek S.

asked • 05/18/18question is- lim_{x=a} x^{5}-a^{5}^{⁄}x^{2}-a^{2}

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Arturo O. answered • 05/18/18

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You can also apply L'Hopital's rule, since the form is indeterminate. You can apply it more than once until you get a determinate form. By the way, you should group things properly in parentheses:

(x^{5} - a^{5})/(x^{2} - a^{2})

I assume that is what you really meant. But for the expression as LITERALLY stated, then you get the result in Alexander's answer.

Arturo O.

Thank you, Alexander.

Unfortunately, there are many math problems on this site that lack proper grouping of expressions, questions with incomplete information, unsolvable problems, ambiguous wording, contradictory information, etc. It is often challenging to figure out what the student really meant to ask. I am sure you will see more of this as time goes by.

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05/18/18

Alexander B. answered • 05/18/18

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There is a trick here!

You will find that (x-a) is a factor of both the numerator and denominator.

Since for purposes of the limit x ≠ a, you can divide out (cancel) the factor x-a.

Then the limit will become obvious, but I will not do it for you...the divisions are good practice in algebraic manipulation.

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Alexander B.

05/18/18