anonymous
  • anonymous
lim x->1 (sqrt(x) - 1)/ (x - 1)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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hartnn
  • hartnn
hint : \((x-1)=(\sqrt x)^2-1^2 \) now use the difference of squares \(a^2-b^2=(a+b)(a-b)\)
anonymous
  • anonymous
how do i do that?
hartnn
  • hartnn
\((x-1)=(\sqrt x)^2-1^2=(\sqrt x-1)(\sqrt x+1)\) got this ? what gets cancelled ?

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More answers

anonymous
  • anonymous
okay the sqrt(x) - 1 gets cancelled
hartnn
  • hartnn
yes, you can directly put x=1 now.
anonymous
  • anonymous
okay so i substitute x = 1 into sqrt(x) - 1?
hartnn
  • hartnn
no....that got cancelled....what remains ?
anonymous
  • anonymous
what remains is (x - 1)
hartnn
  • hartnn
but we wrote x-1 as \((x-1)=(\sqrt x)^2-1^2=(\sqrt x-1)(\sqrt x+1)\)
anonymous
  • anonymous
ok
hartnn
  • hartnn
\(\dfrac{\sqrt x-1}{x-1}=\dfrac{\sqrt{x}-1}{(\sqrt x-1 )(\sqrt x +1)}=\dfrac{1}{\sqrt x+1}\) got this ? now put x=1
anonymous
  • anonymous
ok i get 1/2
hartnn
  • hartnn
i get the same, its correct.
anonymous
  • anonymous
ok i get 1/2
hartnn
  • hartnn
yes, 1/2 is correct.

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