# How do you find the x values at which #f(x)=csc 2x# is not continuous, which of the discontinuities are removable?

##### 1 Answer

It depends...

#### Explanation:

The answer to this question depends on your definition of continuity.

A function

#lim_(x->a) f(x)" "# exists and is equal to#f(a)# .

If it is continuous at every point in its domain then according to at least one definition of continuity, we would say that

By this definition,

The domain of

So

Some authors would say that

#lim_(x->(kpi)^+) csc 2x = +oo != -oo = lim_(x->(kpi)^-) csc 2x#

and:

#lim_(x->(((2k+1)pi)/2)^+) csc 2x = -oo != +oo = lim_(x->(((2k+1)pi)/2)^-) csc 2x#

That is, the left and right limits disagree at the points

Note however that these points are not part of the domain.

graph{csc(2x) [-10, 10, -5, 5]}