# Math Help - L'Hopital's Rule

1. ## L'Hopital's Rule

I need help with these two problems.

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

and

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

2. L'Hopital's rule? I wouldn't use that here...
Originally Posted by CarDoor
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: $\frac 1x - \frac 1{\sqrt x} = \frac {1 - \sqrt x}x$

3. Originally Posted by CarDoor
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 ?

4. For the second one, what did you do to get that?

5. Originally Posted by CarDoor
For the second one, what did you do to get that?
combine the fractions

6. Oh I see. I guess I was thinking too hard. Thanks for the help.