Question

I'm really confused on what the limit would be here:

Answer 1

lim (1)/(x-10)^2 x-->10

Answer 2

I think there's no limit but wolfram says it's -1/90 how is that possible?

Answer 3

Do you accept \(\pm \infty/DNE\)?

Answer 4

What do you mean do I accept those? Yea I've dealt with them before if that's what you mean

Answer 5

http://www.wolframalpha.com/input/?i=lim+%281%29%2F%28x-10%29%5E2+x--%3E10

Answer 6

ohhh I see my mistake but I have to explain why it is infinity

Answer 7

as x->10 x-10 approaches 0

when you square it, you get +0 from either direction
divide by a number that approaches 0 gives you a number that tends to infinity

Answer 8

but isn't 1/0 undefined. that's what confuses me

Answer 9

If you wanna be exact.. \(\lim_{x \rightarrow 10^-} f(x)=\infty \) and \(\lim_{x \rightarrow 10^+} f(x)=\infty \), \(\lim_{x \rightarrow 10^-} f(x)=\lim_{x \rightarrow 10^+} f(x)\) So the limit is \(\infty\) :P

Answer 10

but what makes it infinity like what do you plug in to the equation and how do you expand it

Answer 11

See http://www.khanacademy.org/math/differential-calculus/limits_topic/limits-infinity/v/limits-and-infinity

Answer 12

okay thanks :)

Answer 13

The idea is we do *not* divide by 0. rather, we ask what does the quotient *approach* as x approaches 0.

Answer 14

yea i understood thank you so much