Title MAT 1B JR CONT M02 EX 8 2 PROB(16 Aug 2016).ppt ✅

CONTINUITY
EXAMPLE PROBLEMS
Solution Example1: Show that f(x)=[x] is continuous at only those real numbers that are not integers i.e., on R - Z Let a∈R If a∉Z then [a]≠a ∴ [a]Thus Lt x a f (x) does not exist ∴ ‘f’ is discontinuous at ‘a’ if a∈z ∴ ‘f’ is continuous on R – Z. If a∈Z then and Lt x a+ f (x) =a Lt x a- f (x) = a - 1 Here, L.H.L ≠ R.H.L