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anonymous

  • 5 years ago

Evaluate limit ((x/(1+(sqrtx))-(1/2))/(x-1)

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  1. anonymous
    • 5 years ago
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    as x approaches 1

  2. amistre64
    • 5 years ago
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    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

  3. anonymous
    • 5 years ago
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    I have the answer, I just want to know where I'm going wrong in solving it.

  4. amistre64
    • 5 years ago
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    well then :) ..... whatcha got written?

  5. anonymous
    • 5 years ago
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    So far, I've only combined the numerator.

  6. anonymous
    • 5 years ago
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    Then I get (2x-1-(sqrtx))/(2*(1+(sqrtx)))/(x-1)

  7. anonymous
    • 5 years ago
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    Then I get lost

  8. anonymous
    • 5 years ago
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    I set it up where you should multiply by the reciprocal

  9. anonymous
    • 5 years ago
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    then took the radical outside of the denominator

  10. anonymous
    • 5 years ago
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    now I'm stuck

  11. amistre64
    • 5 years ago
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    \[\frac{\frac{x}{(1+\sqrt{x})}-\frac{1}{2}}{x-1}\] this the function?

  12. anonymous
    • 5 years ago
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    yes

  13. amistre64
    • 5 years ago
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    2x -1 - sqrt(x)) ---------------- right? 2 (1+sqrt(x)) (x-1)

  14. anonymous
    • 5 years ago
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    yes.

  15. amistre64
    • 5 years ago
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    as x-> 1 we need to determine if the top can control it..... does it factor...

  16. anonymous
    • 5 years ago
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    yes, it does.

  17. amistre64
    • 5 years ago
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    what do we get for the top then?

  18. anonymous
    • 5 years ago
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    let me do the quadratic I guess.

  19. anonymous
    • 5 years ago
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    (\[(\sqrt{x}+1)(\sqrt{x}-1/2)\]

  20. anonymous
    • 5 years ago
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    I don't think that's right though?

  21. amistre64
    • 5 years ago
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    2a^2 -a -1 ; a=sqrt(x) (a-2/2)(a+1/2) a = 1, -1/2 sqrt(x) = 1, -1/2; i agree

  22. anonymous
    • 5 years ago
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    oh yes it does. :)

  23. amistre64
    • 5 years ago
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    (sqrt(x)-1) (2sqrt(x)+1) -------------------- 2 (sqrt(x)+1) (x-1) we are closer i think lol

  24. anonymous
    • 5 years ago
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    I still divide by zero.

  25. amistre64
    • 5 years ago
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    gotta go over and make sure I aint missed nuthin

  26. anonymous
    • 5 years ago
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    you cancel out the 2(sqrtx+1) on top and bottom.

  27. amistre64
    • 5 years ago
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    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

  28. anonymous
    • 5 years ago
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    eeek.

  29. amistre64
    • 5 years ago
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    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

  30. amistre64
    • 5 years ago
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    http://www.wolframalpha.com/input/?i=%282%2B2sqrt%28x%29%29%28x-1%29

  31. anonymous
    • 5 years ago
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    woah, ok.

  32. amistre64
    • 5 years ago
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    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...

  33. amistre64
    • 5 years ago
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    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

  34. anonymous
    • 5 years ago
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    Oh well, that's inconsistent with the answer key. But thanks for all your help. :)

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