Question

Is f(x)=1/(x-5) continuous at x=5?

Answer 1

No.

Explanation:

If f(x) is continuous at x = 5, then this must be true:

`lim_(xrarr5^-) f(x)` and `lim_(xrarr5^+) f(x)` must exist and

`lim_(xrarr5^-) f(x) = lim_(xrarr5^+) f(x)`

Here `lim_(xrarr5^-) f(x)` = `1/(5-5)` = `1/0`

So, `lim_(xrarr5^-) f(x)` does not exist.

So f(x) isn't continuous at x = 5.