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Math Help - L'Hopital's Rule

  1. #1
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    L'Hopital's Rule

    I need help with these two problems.

    \lim_{x\to0^+} (lnx-lnsinx)

    and

    \lim_{x\to0^+} \frac{1}{x} - \frac{1}{\sqrt{x}}
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    L'Hopital's rule? I wouldn't use that here...
    Quote Originally Posted by CarDoor View Post
    I need help with these two problems.

    \lim_{x\to0^+} (lnx-lnsinx)
    Hint: lnA - lnB = ln(A/B)

    \lim_{x\to0^+} \frac{1}{x} - \frac{1}{\sqrt{x}}
    Hint: \frac 1x - \frac 1{\sqrt x} = \frac {1 - \sqrt x}x
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  3. #3
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    Quote Originally Posted by CarDoor View Post
    I need help with these two problems.

    \lim_{x\to0^+} (lnx-lnsinx)

    and

    \lim_{x\to0^+} \frac{1}{x} - \frac{1}{\sqrt{x}}
    \lim_{x\to0^+} (lnx-lnsinx)
    =\lim_{x\to0^+}ln(\frac{x}{sinx})
    =ln(\lim_{x\to0^+}\frac{x}{sinx})
    =ln(1)=0


    For the another one:
    \frac{1}{x}-\frac{1}{\sqrt{x}} = \frac{1-\sqrt{x}}{x}

    Got it ?
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  4. #4
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    For the second one, what did you do to get that?
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by CarDoor View Post
    For the second one, what did you do to get that?
    combine the fractions
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  6. #6
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    Oh I see. I guess I was thinking too hard. Thanks for the help.
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