f-x-2-x-3x-x-examine-its-continuity-at-x-1-2-where-x-is-greatest-integer-function-

Question Number 54688 by pooja24 last updated on 09/Feb/19

f (x) = \frac{2 [x]}{3 x - [x]} e x a m i n e i t s c o n t i n u i t y a t x = \frac{- 1}{2}

w h e r e [x] i s g r e a t e s t i n t e g e r f u n c t i o n

Commented by maxmathsup by imad last updated on 10/Feb/19

w e h a v e f (- \frac{1}{2}) = \frac{2 (- 1)}{- \frac{3}{2} - (- 1)} = \frac{- 2}{- \frac{3}{2} + 1} = \frac{- 2}{- \frac{1}{2}} = 4

a n d {l i m}_{x \to {(- \frac{1}{2})}^{+}} f (x) = {l i m}_{x \to {(- \frac{1}{2})}^{-}} f (x) = 4 = f (- \frac{1}{2}) s o f i s c o n t i n u e a t

x_{0} = - \frac{1}{2} .

Answered by kaivan.ahmadi last updated on 09/Feb/19

f (- \frac{1}{2}) = li \underset{x \to - \frac{1^{+}}{2}}{m f} (x) = li \underset{x \to - \frac{1^{-}}{2}}{m f} (x) = 4

so f is continuos at x = - \frac{1}{2}