Show that function ƒ(x) = is continuous.
Given:
ƒ(x) =
Left hand limit and x = 1
=
=
Applying L hospital’s rule
= n
Right hand limit and x = 1
=
=
Applying L hospital’s rule
= n
Also, f(x) = n at x =1
As we can see that
Thus, f(x) is continuous at x = 1