Thread: Limits of a logarithm
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Old December 3rd, 2008, 01:43 AM
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Originally Posted by Bud View Post
Hi folks,

I have some problems with this limit:


I cannot decide which direction to go. The 1+... can be neglected right? Mr F says: Wrong.

But what about the constants in the exponent?

Thanks in advance.
Bud
Start by considering \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] (why is this change of order allowed?) ..... (One of the abvove cases is not valid).
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