Thread: continous function

f(x)=e^-1/x2 if x is not =0
=0 if x=0

then f is continuous. how it can be proved.

Originally Posted by saravananbs

f(x)=e^-1/x2 if x is not =0
=0 if x=0

then f is continuous. how it can be proved.

See if .

Originally Posted by saravananbs

f(x)=e^-1/x2 if x is not =0
=0 if x=0

then f is continuous. how it can be proved.

We need to show that





Now evaluate the limit and show that it equals

yes at x=0, it is continuous

but for other points , how its derived.

is it like limit x-> a+h f(x) = limit x-> a-h f(x) =f(a)?

Originally Posted by saravananbs

yes at x=0, it is continuous

but for other points , how its derived.

One way is to say that is continuous as the composition of continuous functions.

Originally Posted by emakarov

One way is to say that is continuous as the composition of continuous functions.

i think three function are involved , e^x ,1/x, x^2

all are continuous. is it right.

All are continuous where x =/= 0.

Yes, all are continuous for x ≠ 0.