Question

S2, if x is irrational
2. If fis defined on R as f (x) =
1, if x is rational,
lim
f(x) does not exist for any a € R.
X ->a
prove that
iona
1​

Answer 1

Answer:

ANSWER

At x=0

x→0

+

lim

f(x)=0

(Same for rational and irrational)

Also

x→0

−

lim

f(x)=0

So it is continuous at x=0

At other number it's limit is not defined in it's neighbourhood as it can be x or 0 when x



=0 it is not continuous.

So f(x) is continuous only at 0

Answered By