Using L'Hospital's Rule for Indeterminate Form Problems in Calculus

[blu3jam]

Hi I'm new to this forum, i need a help i don't know how can i use l'hospital in these problems;lim(x->1, ((arccos(x))^lnx))

lim(x->\pi/2+ (cosx ln(x - \pi/2 ) )Can anyone help?

 

[nicksauce]

The second one is greatly simplified if you make a change of variables u = x - pi/2

 

[blu3jam]

The second one is greatly simplified if you make a change of variables u = x - pi/2

Thanks, but still i don't know how can i proceed ? =(

lim(u->0+ (cos(u+\pi/2) ln(u ) )

 

[nicksauce]

Well cos(u+pi/2) = -sin(u)

Then you can write your function as
-ln(u) / csc(u), and then apply l'hopital's rule. See where that gets you.

 

[blu3jam]

Well cos(u+pi/2) = -sin(u)

Then you can write your function as
-ln(u) / csc(u), and then apply l'hopital's rule. See where that gets you.

Now ,i figured it out thank you