continous function: f = 1/ln(x) for x neq 0, f = 1 for x = 0

[dopey9]

f:[-1,1] -> R is defined as

.........../ 1/ln(x) , x not equal be 0
f(x) = {
...........\ 0, x=0

How do I show this is continious?
Thanks!

 

[pka]

Ln(x) is not defined for \(\displaystyle x \le 0 .\)

 

[dopey9]

forgot to put the mod sign

sori i forgot to put the modulus sign on ...its meant ot be 1 / ln (|x|)

 

[pka]

\(\displaystyle \L \lim _{x \to 0} \ln \left( {\left| x \right|} \right) = - \infty \quad \Rightarrow \quad \lim _{x \to 0} \frac{1}{{\ln \left( {\left| x \right|} \right)}} = 0\)

Draw a graph. You will see it!