A few days ago
White Infinity

Limit Question?

Hi this question is regarding L’Hopital’s rule.

The limit of x raised to [ 2 / (x-1) ] as x approaches +1.

So basically I can’t plug 1 in for x b/c it givces me 0 on the denominator in the exponent. I know I”m supposed to take the derivative until I can plug in 1 but I’m not sure how to do it.

Top 1 Answers
A few days ago
Susan R

Favorite Answer

The way to look at this is, what would you actually get if x=1? Of course, if you are coming from say 0.99999, you end up having 0.99999 raised to a really large power. So, the .99999 times itself is getting SMALLER. Coming from LESS THAN ONE, you are then approaching zero.

If you come from the opposite direction, though, like 1.00001, you get 1.00001 being raised to a very large exponent, and so the number is getting BIGGER. You would then be approaching infinity.

The problem with taking the derivative is, you will always end up with a zero in the denominator… Meaning always an infinite exponent. And taking the derivative would mean that now you are also multiplying the whole thing by 2/0 (which itself approaches infinity).

So, really it’s not a cut-and-dried answer, but now you can imagine you approach zero from one direction, and infinity from the other — would look something like the graph of the tangent function at 90 degrees!

Hope that helps!

0