# L'Hospital's rule with trigs

• Nov 13th 2012, 02:11 PM
kingsolomonsgrave
L'Hospital's rule with trigs
Hello all!

I need some help with this question:

Attachment 25693

the rule requires f(x)/g(x) to go to an indeterminate form, does that mean I rewrite this as a quotient?

so lim as x-> 0 of the xth root of $(sinx+cosx)$

is that right?
• Nov 13th 2012, 03:16 PM
Chipset3600
Re: L'Hospital's rule with trigs
Quote:

Originally Posted by kingsolomonsgrave
Hello all!

I need some help with this question:

Attachment 25693

the rule requires f(x)/g(x) to go to an indeterminate form, does that mean I rewrite this as a quotient?

so lim as x-> 0 of the xth root of $(sinx+cosx)$

is that right?

if
$y=\lim_{x->0}[cos(x)+sin(x)]^{1/x}$

so: $ln(y)=\lim_{x->0}ln[[cos(x)+sin(x)]^{1/x}]$
Now you most use the logarithmic power rule and you will get indeterminate form: 0/0
• Nov 28th 2012, 07:24 AM
kingsolomonsgrave
Re: L'Hospital's rule with trigs
$ln(y)=$lim as x->0 $ln(sinx/x + cosx/x)$
am I on the right track?
• Nov 28th 2012, 07:55 AM
Scopur
Re: L'Hospital's rule with trigs
Quote:

Originally Posted by kingsolomonsgrave
$ln(y)=$lim as x->0 $ln(sinx/x + cosx/x)$
am I on the right track?

This is not true you cant bring the $\frac{1}{x}$ "into" your ln function. You want to write $\frac{\ln( \sin(x) + \cos(x))}{x}$