L'Hopital's Rule

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January 14th 2010, 01:31 PM
CarDoor

L'Hopital's Rule

I need help with these two problems.

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

and

$\lim_{x\to0^+}$ $\frac{1}{x}$ - $\frac{1}{\sqrt{x}}$
January 14th 2010, 01:36 PM
Jhevon

L'Hopital's rule? I wouldn't use that here...

Quote:

Originally Posted by CarDoor

I need help with these two problems.

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

Hint: lnA - lnB = ln(A/B)

Quote:

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

Hint: $\frac 1x - \frac 1{\sqrt x} = \frac {1 - \sqrt x}x$
January 14th 2010, 01:39 PM
General

Quote:

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 ?
January 14th 2010, 02:00 PM
CarDoor

For the second one, what did you do to get that?
January 14th 2010, 02:22 PM
Jhevon

Quote:

Originally Posted by CarDoor

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

combine the fractions
January 14th 2010, 02:33 PM
CarDoor

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

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