anonymous
  • anonymous
lim x->1 (x-1)/ (sqrt(x+3)-2)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
If you know how to take derivatives, L'Hopital's rule makes it easy. Otherwise, multiply by the conjugate.
anonymous
  • anonymous
|dw:1378701120844:dw|
anonymous
  • anonymous
Ya I know how to take derivatives but I am supposed to be doing it the method of using conjugates

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anonymous
  • anonymous
which I am unsure how to do the conjugate of this one
anonymous
  • anonymous
rationalise.
anonymous
  • anonymous
Multiply the numerator and denominator by sqrt(x + 3) + 2)
anonymous
  • anonymous
|dw:1378701255909:dw|
anonymous
  • anonymous
yes i have done this and got x+3-4 for the denominator which is equal to (x+1) but I am not sure how to go about multiplying or simplifying the numerator
anonymous
  • anonymous
If you go to the last answer of this question http://openstudy.com/study#/updates/522d3c65e4b0fbf34d634ab4 I wrote one of these out in full for someone earlier.
anonymous
  • anonymous
If that doesn't help I can write it out for this one specifically if you need it.
anonymous
  • anonymous
yes please because i still dont understand
anonymous
  • anonymous
Sorry, I'm back. Multiply by the conjugate but don't expand the top as you'll need the (x - 1). Multiply the bottom out and you'll end up with (x - 1) which can then cancel with the top. This gives you sqrt(x + 3) + 2 which means the limit is 4.
anonymous
  • anonymous
\[\frac{ x-1 }{ \sqrt{x+3} - 2 } * \frac{ \sqrt{x+3} + 2 }{ \sqrt{x+3} + 2 } = \frac{ (x-1) * (\sqrt{x+3} + 2) }{ (\sqrt{x+3} - 2)*(\sqrt{x+3} + 2) }\] \[\frac{ (x-1) * (\sqrt{x+3} + 2) }{ (\sqrt{x+3} - 2)*(\sqrt{x+3} + 2) } = \frac{ (x-1) * (\sqrt{x+3} + 2) }{ (x - 1) }\] \[\lim_{x \rightarrow 1} \sqrt{x+3} + 2 = 4\]
anonymous
  • anonymous
Okay I understand now thank you so much

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