lim [ln(x^4-3)]/[ln(x)cos(1/x)]

x-> INF

So, that is the form INF/INF, so I tried to take the derivative of the numerator and denominator, but I can't figure out the derivative of the denominator.

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- Nov 18th 2007, 07:04 AMsiriano.3l'Hôpital's Rule
lim [ln(x^4-3)]/[ln(x)cos(1/x)]

x-> INF

So, that is the form INF/INF, so I tried to take the derivative of the numerator and denominator, but I can't figure out the derivative of the denominator. - Nov 18th 2007, 07:07 AMJhevon
- Nov 18th 2007, 09:32 AMThePerfectHacker
since . This problem reduces to:

.

We can solve this without L'Hopital, note when is large:

Thus,

.

Now the left side and right side limits are 4, because, for example,

.

But,

.