f-x-1-x-if-x-lt-1-2x-1-if-x-gt-1-investigate-the-existence-and-non-existence-of-the-limit-of-f-at-the-point-x-1-

Question Number 73570 by Rio Michael last updated on 13/Nov/19

f : x \to {\begin{cases} 1 + x, i f x < 1 \\ 2 x - 1, i f x > 1 \end{cases}

i n v e s t i g a t e t h e e x i s t e n c e a n d n o n e x i s t e n c e o f t h e

l i m i t o f f a t t h e p o i n t x = 1

Commented by kaivan.ahmadi last updated on 13/Nov/19

{l i m}_{x \to 1^{-}} f (x) = {l i m}_{x \to 1^{-}} (1 + x) = 2

{l i m}_{x \to 1^{+}} f (x) = {l i m}_{x \to 1^{+}} (2 x - 1) = 1

\Rightarrow {l i m}_{x \to 1^{-}} f (x) \neq {l i m}_{x \to 1^{+}} f (x) \Rightarrow

{l i m}_{x \to 1} f (x) i s n o t e x i s t .