anonymous
  • anonymous
How would you solve lim(x->5)[(x-5)/((√x-1)-2)]?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
Trying to solve this directly you get lim(x -> 5)(f(x)) = 0/0 therefore, you can apply L'Hopital's rule. Taking the derivative of the top and the bottom, you get lim(x -> 5)(f(x)) = lim(x -> 5)(1/(1/(2*sqrt(x-1)))) = lim(x -> 5)(2*sqrt(x-1)). Putting x into this equation, you get lim(x -> 5)(f(x)) = 4
anonymous
  • anonymous
How does the bottom equal 1/(2xsqrt(x-1))? If the bottom is (sqrt(x-1) -2, how does a 2 get in front of the sqrt? I got 1/2(x-1)^(-1/2)
anonymous
  • anonymous
Exactly, that is in the denominator 1/(1/2*(x-1)^(-1/2)) so move it all to the top canceling the 1's and you get 2*sqrt(x-1)

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anonymous
  • anonymous
I finally figured out how that makes sense! My head just exploded but its all good. Thank you :)

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