If is continuous for real x, then
Continuity at a point -
A function f(x) is said to be continuous at x = a in its domain if
1. f(a) is defined : at x = a.
of f(x) at x = a exists from left and right.
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Properties of Continuous function -
If are two continuous functions at a point a of their common domain D.Then fg are continuous at a and if then
is also continuous at x = a.
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(sin kx)p is continuous and differentiable function x R , k R and p > 0.
[x] is discoutinuous at x I
For
and
So f (x) becomes coutinuous for all x R
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