Quote:
Originally Posted by mr fantastic  Start by considering ![\lim_{z \rightarrow + \infty} \left[ 1 + C e^{A(z-B)}\right]](http://www.mathhelpforum.com/math-help/latex2/img/9bdf035b9790537ec8cc2758468be0e6-1.gif "\lim_{z \rightarrow + \infty} \left[ 1 + C e^{A(z-B)}\right]") : C > 0:
A > 0: The limit is equal to +oo.
A < 0: The limit is equal to 1. C < 0:
A < 0: The limit is equal to 1.
A > 0: The limit is equal to -oo.
Now consider ![\ln \lim_{z \rightarrow + \infty} \left[ 1 + C e^{A(z-B)}\right]](http://www.mathhelpforum.com/math-help/latex2/img/0deafd1676a2a5c072dfc78a7a217f67-1.gif "\ln \lim_{z \rightarrow + \infty} \left[ 1 + C e^{A(z-B)}\right]") (why is this change of order allowed?) ..... (One of the abvove cases is not valid). |
Hi,
we can stick to the case C>0, A>0. I have a physical problem here and I know that the constants are always positive. This leaves us with: The limit is equal to +oo.
I do not know why the change of order is allowed. The case for which the change is not valid is the case when the limit goes to -oo. Here the logarithm is not defined.