Improper Integrals and Limits

[Annienakki]

Hi Guys,

I don't have a specific problem I'm working on, just a general question....

We're currently working on evaluating improper integrals in my Calc. II class and I understand the process so far. What's getting me hung up is remembering the rules for resolving limits! It's been too long since Calc. I, I guess....heh...

Anyway, I've brushed up a bit by reading my old textbook and Calculus for Dummies and I'm remembering all the old things like the lim sinx/x=1 and that 1/x tends toward zero when x approaches infinity, but does the limit as x approaches infinity in ln|x+1| tend toward infinity?

Actually I can give you a specific example of what my problem is....I have this:

lim as t->infinity [ ln|t+1|-ln|t+2|+ln2 ]

Now I think this would be divergent because as t gets larger the logs get larger....but the given answer to this problem is ln2 and I just don't see it....any ideas what I'm missing?

Thanks,

Annie

 

[galactus]

Using the log laws.

\(\displaystyle ln(t+1)-ln(t+2)+ln(2)=ln(2)+ln\left(\frac{t+1}{t+2}\right)\)

Now, \(\displaystyle ln\left(\lim_{t\to {\infty}}\frac{t+1}{t+2}\right)=ln(1)=0\)

See now?.

 

[Annienakki]

Thanks for the quick response, Galactus! I get it....Now I am double checking my evaluations by doing a table on my calculator...

What I need to do is go back and just do some limit probs just to refresh my airhead brain, lol...I'm doing fine with the improper integrals, I just have a bad habit of forgetting things I haven't used in a few months...oh well, practice makes perfect....

Thanks again,

Annie