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

Question

gorica · Answer

$$f(x)=(x-3)\ln^2(x-3)$$

cwrw238 · Answer

Hint - what is the value of ln 0?

gorica · Answer

- infinity

anonymous · Answer

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

anonymous · Answer

Try to find this line...

gorica · Answer

I did it using L'Hospital's rule

gorica · Answer

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?

cwrw238 · Answer

yes

gorica · Answer

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