anonymous
  • anonymous
\[\lim x \rightarrow1 t+1 /(t-1)^2\]
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\lim_{t \rightarrow 1}{t+1 \over (t-1)^2}=\infty\]
anonymous
  • anonymous
yep! How'd you get it?
anonymous
  • 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.

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anonymous
  • anonymous
I thought I'd have to factor it and get a real non-zero answer at first.
anonymous
  • anonymous
when do you factor and try to get a non-zero denominator then?
anonymous
  • anonymous
what?
anonymous
  • anonymous
differentiate top and bottom :|
anonymous
  • anonymous
you can't differentiate top and bottom
anonymous
  • anonymous
its in the limits section, so not up to that yet.
anonymous
  • anonymous
you can't apply l'hopital because it's not 0/0
anonymous
  • anonymous
ohh yeh, twice and its zero lol
anonymous
  • anonymous
You should try factoring when you have a \(\frac{0}{0}\) or a \(\frac{\infty}{0}\) or a similar form.
anonymous
  • anonymous
oh -- thank you. I've been factoring whenever I get 0 in the denominator.

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