Of an indeterminate form 0/0

• Nov 7th 2010, 01:57 PM
courteous
Of an indeterminate form 0/0
$\displaystyle{ \lim_{z\to z_p} \frac{z^{2m+1}-z_pz^{2m}}{1+z^{2n}} }$
Is this limit really of a indeterminate form 0/0: numerator goes to zero, what about denominator?
• Nov 7th 2010, 03:15 PM
TheEmptySet
Quote:

Originally Posted by courteous
$\displaystyle{ \lim_{z\to z_p} \frac{z^{2m+1}-z_pz^{2m}}{1+z^{2n}} }$
Is this limit really of a indeterminate form 0/0: numerator goes to zero, what about denominator?

No it is not an indeterminate form. As you said the numerator goes to zero, but the denominator is always greater than or equal to 1. (at least over the real numbers.)
• Nov 7th 2010, 11:02 PM
courteous
Quote:

Originally Posted by TheEmptySet
(at least over the real numbers.)

Well, both $z$ and $z_p \in \mathbb{C}$. Does that change anything?