Given-f-x-ln-x-x-1-a-find-the-domain-of-f-b-find-the-limts-of-f-at-the-boundary-of-its-domain-hence-state-the-asymptote-of-y-f-x-

Question Number 95677 by Rio Michael last updated on 26/May/20

Given f (x) = \frac{\ln x}{x - 1}

(a) find the domain of f .

(b) find the limts of f at the boundary of its domain

hence state the asymptote of y = f (x) .

Answered by mathmax by abdo last updated on 27/May/20

1) D_{f} =] 0, 1 [\cup] 1, + \infty [

2) \lim_{x \to o^{+}} f (x) = + \infty and \lim_{x \to 1^{+}} f (x) = \lim_{x \to 1} f (x) = 1

\lim_{x \to + \infty} f (x) = \lim_{x \to + \infty} \frac{lnx}{x (1 - x^{- 1})} = \lim_{x \to + \infty} \frac{lnx}{x} = 0 \Rightarrow

y = 0 is assymtote for C_{f}

Commented by Rio Michael last updated on 27/May/20

thank you so much sir .