Thread: L'Hopital's rule

Hi,
Why can't i use L'Hopital's rule in this limit:

lim (2x+sin2x+1)/(2x+sin2x)(sinx+3)^2 as x->infinity

Thanks...

Originally Posted by Tom92

Hi,
Why can't i use L'Hopital's rule in this limit:

lim (2x+sin2x+1)/(2x+sin2x)(sinx+3)^2 as x->infinity

Thanks...

I assume this is

.

You can only use L'Hospital's Rule if you get or from direct substitution.

But in this case, you'll get .

Originally Posted by Prove It

I assume this is

.

You can only use L'Hospital's Rule if you get or from direct substitution.

But in this case, you'll get .

Dear Prove It,

I think you have made mistake in this case. Note that the limit goes to "infinity". Hence the denominator and numerator both tends to "infinity."

Originally Posted by Sudharaka

Dear Prove It,

I think you have made mistake in this case. Note that the limit goes to "infinity". Hence the denominator and numerator both tends to "infinity."

Oh, oops. Hahaha, I subsituted instead.

Then I don't see why you can't use L'Hospital's Rule in this case...

Originally Posted by Prove It

Oh, oops. Hahaha, I subsituted instead.

Then I don't see why you can't use L'Hospital's Rule in this case...

Dear Prove It,

But notice that,



Dividing the numerator and denominator by "2x";



Therefore the limit does not exist.