Please help evaluate the following expression. It seems that it is 0. But I have no clue how that happens.

(log is based on e. don't know about the constraints about a and b. Let's assume they are not 0s).

Please help evaluate the following expression. It seems that it is 0. But I have no clue how that happens.

(log is based on e. don't know about the constraints about a and b. Let's assume they are not 0s).

(log is based on e. don't know about the constraints about a and b. Let's assume they are not 0s).

I assume that the second term has a log in front of it as well?

The quickest solution is probably to observe that , which shows that the limit you care about is zero.

Alternatively, you could start by rewriting the expression as the log of a fraction, interchange the limit and the log and then show that the limit of the fraction is 1:

The quickest solution is probably to observe that , which shows that the limit you care about is zero.

Alternatively, you could start by rewriting the expression as the log of a fraction, interchange the limit and the log and then show that the limit of the fraction is 1:

owlpride wrote:I assume that the second term has a log in front of it as well?

The quickest solution is probably to observe that , which shows that the limit you care about is zero.

Alternatively, you could start by rewriting the expression as the log of a fraction, interchange the limit and the log and then show that the limit of the fraction is 1:

Thanks for helping me out again, owlpride. I should have put a big parentheses for these two terms.

The key lies in this thing . Is this a common rule or something that obvious? That's where I got stuck. Could you also show some intermediate steps?

Hom wrote:owlpride wrote:I assume that the second term has a log in front of it as well?

The quickest solution is probably to observe that , which shows that the limit you care about is zero.

Alternatively, you could start by rewriting the expression as the log of a fraction, interchange the limit and the log and then show that the limit of the fraction is 1:

Thanks for helping me out again, owlpride. I should have put a big parentheses for these two terms.

The key lies in this thing . Is this a common rule or something that obvious? That's where I got stuck. Could you also show some intermediate steps?

Sorry, my bad. There is another condition, a>0 and b>0. in this case, it's obvious .

I think that you meant lim ax, not ax

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