anonymous
  • anonymous
Evaluate limit ((x/(1+(sqrtx))-(1/2))/(x-1)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
as x approaches 1
amistre64
  • amistre64
1/2 maybe http://www.wolframalpha.com/input/?i=limit{x+to+0}%28%28x%2F%281%2B%28sqrtx%29%29-%281%2F2%29%29%2F%28x-1%29
anonymous
  • anonymous
I have the answer, I just want to know where I'm going wrong in solving it.

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amistre64
  • amistre64
well then :) ..... whatcha got written?
anonymous
  • anonymous
So far, I've only combined the numerator.
anonymous
  • anonymous
Then I get (2x-1-(sqrtx))/(2*(1+(sqrtx)))/(x-1)
anonymous
  • anonymous
Then I get lost
anonymous
  • anonymous
I set it up where you should multiply by the reciprocal
anonymous
  • anonymous
then took the radical outside of the denominator
anonymous
  • anonymous
now I'm stuck
amistre64
  • amistre64
\[\frac{\frac{x}{(1+\sqrt{x})}-\frac{1}{2}}{x-1}\] this the function?
anonymous
  • anonymous
yes
amistre64
  • amistre64
2x -1 - sqrt(x)) ---------------- right? 2 (1+sqrt(x)) (x-1)
anonymous
  • anonymous
yes.
amistre64
  • amistre64
as x-> 1 we need to determine if the top can control it..... does it factor...
anonymous
  • anonymous
yes, it does.
amistre64
  • amistre64
what do we get for the top then?
anonymous
  • anonymous
let me do the quadratic I guess.
anonymous
  • anonymous
(\[(\sqrt{x}+1)(\sqrt{x}-1/2)\]
anonymous
  • anonymous
I don't think that's right though?
amistre64
  • amistre64
2a^2 -a -1 ; a=sqrt(x) (a-2/2)(a+1/2) a = 1, -1/2 sqrt(x) = 1, -1/2; i agree
anonymous
  • anonymous
oh yes it does. :)
amistre64
  • amistre64
(sqrt(x)-1) (2sqrt(x)+1) -------------------- 2 (sqrt(x)+1) (x-1) we are closer i think lol
anonymous
  • anonymous
I still divide by zero.
amistre64
  • amistre64
gotta go over and make sure I aint missed nuthin
anonymous
  • anonymous
you cancel out the 2(sqrtx+1) on top and bottom.
amistre64
  • amistre64
2x - sqrt(x)) -1 ---------------- 2 (1+sqrt(x)) (x-1) (sqrt.x -1)(2sqrt.x +1) -------------------- (sqrt.x +1) (2x-2) (sqrt.x -1)(2sqrt.x +1) ------------------------ 2x sqrt(x) -2sqrt(x) +2x -2 (sqrt.x -1)(2sqrt.x +1) ------------------------ 2(x sqrt(x) -sqrt(x) +x -1) this is my thougths so far; the bottom factors by grouping maybe
anonymous
  • anonymous
eeek.
amistre64
  • amistre64
2[sqrt(x)(x-1) + 1(x-1)] 2 (sqrt(x)+1) (x-1).... somehow this converts to: 2(sqrt(x)-1)(sqrt(x)+1)^2
amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=%282%2B2sqrt%28x%29%29%28x-1%29
anonymous
  • anonymous
woah, ok.
amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=lim{x+to+1}%28%28x%2F%281%2B%28sqrtx%29%29-%281%2F2%29%29%2F%28x-1%29 this shows steps...
amistre64
  • amistre64
i dont know why it cuts the link short in firefox.... but copy paste that into the address bar and you shouldbe able to see how they stepped thru it
anonymous
  • anonymous
Oh well, that's inconsistent with the answer key. But thanks for all your help. :)

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