anonymous
  • anonymous
lim x->1 (sqrt(x) - 1)/ (x - 1)
Mathematics
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anonymous
  • anonymous
lim x->1 (sqrt(x) - 1)/ (x - 1)
Mathematics
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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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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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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