anonymous
  • anonymous
What is the limit as x approaches a of x-a/√x-√a
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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sirm3d
  • sirm3d
\[\frac{x-a}{\sqrt{x}-\sqrt{a}}=\frac{x-a}{\sqrt{x}-\sqrt{a}}.\frac{\sqrt{x}+\sqrt{a}}{\sqrt{x}+\sqrt{a}}\]
sohailiftikhar
  • sohailiftikhar
its quite simple ...
sohailiftikhar
  • sohailiftikhar
you can solve it by trick ..

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sohailiftikhar
  • sohailiftikhar
take derivative of above and below saperately then put the limit in answer ...
johnweldon1993
  • johnweldon1993
\[\large \lim_{x\rightarrow a}\frac{x-a}{\sqrt{x} - \sqrt{a}}\] Becomes 0/0 so we can take the derivative of the top wrt 'a' and the the derivative of the bottom wrt 'a' \[\large \frac{-1}{-\frac{1}{2}a^{-1/2}}\] \[\large \frac{-1}{\frac{-1}{-2\sqrt{a}}}\] Which will come out to \(\large 2\sqrt{a}\)
johnweldon1993
  • johnweldon1993
*accidentally put a 2nd negative sign in the bottom fraction...only supposed to be one negative...answer remains the same however
sohailiftikhar
  • sohailiftikhar
yes it will be \[2\sqrt{a}\]
Loser66
  • Loser66
I prefer @sirm3d method.
sohailiftikhar
  • sohailiftikhar
as you wish but if you have to solve extensive Q you should now the tricks also ...

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