Show that the function F(x) = is
Neither continuous and nor differentiable, if m≤0.

Question

Show that the function F(x) = is Neither continuous and nor differentiable, if m≤0.

Philoid · Accepted Answer

LHL =

=

= Not defined, as m 0

RHL =

=

= Not Defined, as

Since, LHL and RHL are not Defined ,So f(x) is not continuous.

Let x = 0 for

Now,

(LHD at x = 0) =

=

= Not Defined , as

(RHD at x = 0) =

=

= Not Defined , as

Hence, f(x) is not differentiable at x = 0 for

Show that the function F(x) = isNeither continuous and nor differentiable, if m≤0.