anonymous
  • anonymous
Find the limit as x approaches 4, using an algebraic method (not derivation). [sqrt(x^2-1)-sqrt(15)]/(x-4)
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
|dw:1327344927815:dw|
anonymous
  • anonymous
Drawing is for clarification.
anonymous
  • anonymous
multiply top and bottom by \[\sqrt{x^2-1}+15\]and you will get it quickly

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anonymous
  • anonymous
numerator will be \[x^2-16=(x+4)(x-4)\] cancel with the x - 4 in the denominator, then replace x by 4
anonymous
  • anonymous
What about the denominator?
anonymous
  • anonymous
So it will be (4+4)/(sqrt(15)+sqrt(15)
anonymous
  • anonymous
That will equal 8/sqrt(30) which isn't the answer I found on wolfram or anything else. All other programs say the answer is 4/sqrt(15)
myininaya
  • myininaya
you have a mistake in simplifying
myininaya
  • myininaya
\[\frac{8}{2 \sqrt{15}} =\frac{4}{\sqrt{15}}\]

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