lim-x-2-ln-2x-10-x-2-

Question Number 106435 by Study last updated on 05/Aug/20

l i \underset{x \to 2}{m} \frac{l n (2 x + 10)}{x - 2} = ? ?

Commented by Dwaipayan Shikari last updated on 05/Aug/20

l i m i t {d o e s n}^{'} t e x i s t

Commented by bemath last updated on 05/Aug/20

\ln (14) \neq 0 . so L^{'} Hopital rule {doesn}^{'} t

work .

Answered by 1549442205PVT last updated on 05/Aug/20

Set x - 2 = t we get l i \underset{x \to 2}{m} \frac{l n (2 x + 10)}{x - 2} =

\lim_{x \to 2} \frac{\ln [2 (x - 2) + 14]}{x - 2} = \lim_{t \to 0} \frac{\ln (2 t + 14)}{t}

\underset{Hopital}{=} \lim_{t \to 0} \frac{2}{2 t + 14} = \frac{2}{14} = \frac{1}{7}

Commented by Her_Majesty last updated on 05/Aug/20

y o u c a n n o t u s e l^{'} H o p i t a l i n t h i s c a s e b e c a u s e

l n (2 t + 14) i s d e f i n e d f o r t = 0

Commented by 1549442205PVT last updated on 05/Aug/20

Thank you Sir . I mistaked . That limit

lead to \infty