Of an indeterminate form 0/0

Printable View

November 7th 2010, 12:57 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?
November 7th 2010, 02:15 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.)
November 7th 2010, 10:02 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?

All times are GMT -8. The time now is 01:46 AM.

Copyright © 2005-2013 Math Help Forum. All rights reserved.

Copyright © 2005-2013 Math Help Forum. All rights reserved.