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anonymous

  • one year ago

What is the limit as x approaches a of x-a/√x-√a

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  1. sirm3d
    • one year ago
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    \[\frac{x-a}{\sqrt{x}-\sqrt{a}}=\frac{x-a}{\sqrt{x}-\sqrt{a}}.\frac{\sqrt{x}+\sqrt{a}}{\sqrt{x}+\sqrt{a}}\]

  2. sohailiftikhar
    • one year ago
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    its quite simple ...

  3. sohailiftikhar
    • one year ago
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    you can solve it by trick ..

  4. sohailiftikhar
    • one year ago
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    take derivative of above and below saperately then put the limit in answer ...

  5. johnweldon1993
    • one year ago
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    \[\large \lim_{x\rightarrow a}\frac{x-a}{\sqrt{x} - \sqrt{a}}\] 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 \(\large 2\sqrt{a}\)

  6. johnweldon1993
    • one year ago
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    *accidentally put a 2nd negative sign in the bottom fraction...only supposed to be one negative...answer remains the same however

  7. sohailiftikhar
    • one year ago
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    yes it will be \[2\sqrt{a}\]

  8. Loser66
    • one year ago
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    I prefer @sirm3d method.

  9. sohailiftikhar
    • one year ago
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    as you wish but if you have to solve extensive Q you should now the tricks also ...

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