Question

Can u plz prove this accordingly?

Answer 1

This is kind of very basic question belonging to limits chapter. We just require to check if RHL = LHL or not,if yes then limit exists else it DNE. There's really nothing as such complicated to show or prove.

Since the piece wise defined f(x) has a modulus involved when x ≠ 0,we need to see how the function will behave at x > 0 and x < 0.

f (x) = x - x/ x for x > 0

f(x) = x + x /x for x < 0

and f (x) = 2 for x = 0

Now, let's find the RHL and LHL and see if the RHL = LHL or not.

RHL :

For lim x → 0+ :

=> x-x/x

=> 0

So,RHL = 0

Now let's check LHL,

For lim x → 0-

=> x + x/x

=> 2x/x

=> 2

So,RHL = 0 and LHL = 2,which concludes RHL ≠ LHL.

•°• lim x → 0 f(x) does not exist.