determine-whether-or-not-lim-x-0-is-continuous-

Question Number 46060 by samitoh last updated on 20/Oct/18

d e t e r m i n e w h e t h e r o r n o t \lim_{x \to 0} [

i s c o n t i n u o u s

Answered by tanmay.chaudhury50@gmail.com last updated on 20/Oct/18

a f u n c t i o n f (x) w i l l b e c o n t i n u o u s a t x = a

w h e n \lim_{x \to a -} f (x) = \lim_{x \to a +} f (x) = f (a)

\lim_{x \to 4 -} f (x)

= \lim_{x \to 4 -} \frac{x^{2} - 16}{x - 4}

= \lim_{x \to 4 -} \frac{(x + 4) (x - 4)}{x - 4} = 4 + 4 = 8

\lim_{x \to 4 +} f (x)

= \lim_{x \to 4 +} \frac{x^{2} - 16}{x - 4}

= \lim_{x \to 4 +} \frac{(x + 4) (x - 4)}{x - 4} = 4 + 4 = 8

f (4) = 8 s o f (x) c o n t i n u o u s a t x = 4