Question

Can you find asymptotes of the function
f(x)=(x-3)(ln(x-3))^2

Answer 1

\[f(x)=(x-3)\ln^2(x-3)\]

Answer 2

Hint - what is the value of ln 0?

Answer 3

- infinity

Answer 4

a line that draws increasingly nearer to a curve without ever meeting it shows the asymptote of that curve.

Answer 5

Try to find this line...

Answer 6

I did it using L'Hospital's rule

Answer 7

Is it? Domain is \[(3,+\infty)\]The function is positive at the whole domain, increasing at the beginning, than decreasing and then increasing again... I would say that it doesn't have a vertical asymptote. Also, \[\lim_{x \rightarrow 3+}(x-3)\ln^2 (x-3)=0\] which means that this function does not have a vertical asymptote. Am I right?

Answer 8

yes

Answer 9

Yes, it is (answer on the first question) or yes, I am right (answer on the second question)?