I need help with these two problems.

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

and

$\displaystyle \lim_{x\to0^+}$ $\displaystyle \frac{1}{x}$ - $\displaystyle \frac{1}{\sqrt{x}}$

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- Jan 14th 2010, 01:31 PMCarDoorL'Hopital's Rule
I need help with these two problems.

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

and

$\displaystyle \lim_{x\to0^+}$ $\displaystyle \frac{1}{x}$ - $\displaystyle \frac{1}{\sqrt{x}}$ - Jan 14th 2010, 01:36 PMJhevon
- Jan 14th 2010, 01:39 PMGeneral
$\displaystyle \lim_{x\to0^+}$ $\displaystyle (lnx-lnsinx)$

$\displaystyle =\lim_{x\to0^+}ln(\frac{x}{sinx})$

$\displaystyle =ln(\lim_{x\to0^+}\frac{x}{sinx})$

$\displaystyle =ln(1)=0$

For the another one:

$\displaystyle \frac{1}{x}-\frac{1}{\sqrt{x}} = \frac{1-\sqrt{x}}{x}$

Got it ? - Jan 14th 2010, 02:00 PMCarDoor
For the second one, what did you do to get that?

- Jan 14th 2010, 02:22 PMJhevon
- Jan 14th 2010, 02:33 PMCarDoor
Oh I see. I guess I was thinking too hard. Thanks for the help.