## anonymous 5 years ago $\lim x \rightarrow1 t+1 /(t-1)^2$

1. anonymous

$\lim_{t \rightarrow 1}{t+1 \over (t-1)^2}=\infty$

2. anonymous

yep! How'd you get it?

3. anonymous

Plugging $$t=1$$ gives $$\frac{2}{0}$$, which in undefined. Whenever you have a number other than $$0$$,over $$0$$ then the limit goes to $$\infty$$ or$$- \infty$$. All you have to do is to test the sign around $$1$$, and you can see it's positive as x approaches 1 from both sides.

4. anonymous

I thought I'd have to factor it and get a real non-zero answer at first.

5. anonymous

when do you factor and try to get a non-zero denominator then?

6. anonymous

what?

7. anonymous

differentiate top and bottom :|

8. anonymous

you can't differentiate top and bottom

9. anonymous

its in the limits section, so not up to that yet.

10. anonymous

you can't apply l'hopital because it's not 0/0

11. anonymous

ohh yeh, twice and its zero lol

12. anonymous

You should try factoring when you have a $$\frac{0}{0}$$ or a $$\frac{\infty}{0}$$ or a similar form.

13. anonymous

oh -- thank you. I've been factoring whenever I get 0 in the denominator.