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
?

1 Answer
Sep 12, 2017

#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.#