Question

Examine continuity of function f(x) =( (e^1/x)-1))/((e^1/x)+1)) at x=0 ?

Examine continuity of function f(x) =( (e^1/x)-1))/((e^1/x)+1)) at x=0
?

Answer 1

`f` is not continuous at `x=0.`

Explanation:

By the Defn. of Continuity,

A function `f` is continuous at `x=0,` if and only if,

`lim_(x to 0-) f(x)=f(0)=lim_(x to 0+) f(x).`

Observe that, `f` is not defined at `x=0.`

Therefore, `f` can not be continuous at `x=0.`