Question

consider the function f(x) = [x].
find limt x

al
and lim Rex I and ein Fea)?
->
b)
show that fel) is discontinuos at every
integers​

Answer 1

Step-by-step explanation:

The given function g(x) is defined at all integral points.

Let n be an integer.

Then g(n)=n−n=n−n=0

L.H.L. at x=n=lim

x→n

−

g(x)=lim

x→n

−

(x−[x])=n−(n−1)=1

R.H.L. at x=n=lim

x→n

+

g(x)=lim

x→n

+

(x−[x])=n−n=0

Since L.H.L.



=R.H.L.

Therefore g is not continuous at x=n. i.e., g(x) is discontinuous at all integral points