Question

How to prove that f(x) is continuous using Left and Right hand limit ?​

Answer 1

to prove f(x) is continuous we have

to do following thing

for given f(x) at a=0

1) weather f(x) is define at x=a or not

2)if f(x) is define x=a find f(a)

3)find LHL by

lim x tends to a-0 f(x)

4)find RHL

lim x tends to a +0

if

f(a) = RHL=LHL

then we say that f(x) is continuous at x=a

now explanation

it was discussed that we approach a point in two way to if both lie we say that it is continuous if not then discontiuous

we use x tends to a-0 why?

ans

here we approach from left hand side in number line it is less then 0 always ( for understanding only) so we use negative one

in RHL we use + sign

because in number line it is always positive

generally there is many different type questions and explanations in

continuity so it is the basic one only