Show that f(x)= { (e1/x -1)/(e1/x +1) , x not equal to 0 is discontinuous at x=0 0 , - Maths - Continuity and Differentiability

Question

Show that f(x)=
{ (e1/x -1)/(e1/x +1) , x not equal to 0
is discontinuous at x=0
0 , x=0

Vipin Verma · Accepted Answer

When x tends to zero from positive side , then 1x will tends to infinity ,When x  tends to zero from negative side , then 1x will tends to  -∞, So checking the continuity , we havelimx→0+ e1/x-1e1/x+1 =limx→0- 1-1/e1/x1+1/e1/x = 1-01+0= 1And when limx→0- e1/x-1e1/x+1 =0-10+1 = -1 Here e-∞ = 0 and e∞ =∞So LHL is not equal to RHL So the function is not contiuous

Show that f(x)= { (e1/x -1)/(e1/x +1) , x not equal to 0 is discontinuous at x=0. 0 , x=0

Show that f(x)=

{ (e^1/x -1)/(e^1/x +1) , x not equal to 0 is discontinuous at x=0.

0 , x=0