onegirl
lim x>1 (sqrt(x)  1)/ (x  1)



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hartnn
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hint :
\((x1)=(\sqrt x)^21^2 \)
now use the difference of squares \(a^2b^2=(a+b)(ab)\)

onegirl
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how do i do that?

hartnn
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\((x1)=(\sqrt x)^21^2=(\sqrt x1)(\sqrt x+1)\)
got this ? what gets cancelled ?

onegirl
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okay the sqrt(x)  1 gets cancelled

hartnn
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yes, you can directly put x=1 now.

onegirl
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okay so i substitute x = 1 into sqrt(x)  1?

hartnn
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no....that got cancelled....what remains ?

onegirl
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what remains is (x  1)

hartnn
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but we wrote x1 as
\((x1)=(\sqrt x)^21^2=(\sqrt x1)(\sqrt x+1)\)

onegirl
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ok

hartnn
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\(\dfrac{\sqrt x1}{x1}=\dfrac{\sqrt{x}1}{(\sqrt x1 )(\sqrt x +1)}=\dfrac{1}{\sqrt x+1}\)
got this ?
now put x=1

onegirl
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ok i get 1/2

hartnn
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i get the same, its correct.

onegirl
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ok i get 1/2

hartnn
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yes, 1/2 is correct.