lim-x-0-ln-x-cot-x-

Question Number 92056 by john santu last updated on 04/May/20

\lim_{x \to 0^{+}} \frac{\ln (x)}{\cot x}

Commented by Prithwish Sen 1 last updated on 05/May/20

\lim_{x \to 0} x . \frac{\underset{k = 1}{\sum^{\infty}} {(- 1)}^{k + 1} \frac{{(x - 1)}^{k}}{k}}{1 - \underset{k = 1}{\sum^{\infty}} \frac{2^{2 k}}{(2 k)!} ∣ B_{2 k} ∣ x^{2 k}} = \frac{0}{1 - 0} = 0

Commented by mathmax by abdo last updated on 04/May/20

f (x) = \frac{l n x}{c o t a n x} \Rightarrow f (x) = l n (x) . t a n x = \frac{s i n x l n x}{c o s x}

s i n x l n x \sim x l n (x) \to 0 (x \to 0) a n d c o s x \sim 1 \Rightarrow

{l i m}_{x \to 0^{+}} f (x) = 0