Determine the points at which the function ƒ is discontinuous and state the type of discontinuity.

Question

Suppose that f(x)= {sin(1/3x) for x ≠ 3}

0 for x = 3

Determine the points at which the function ƒ is discontinuous and state the type of discontinuity.

ƒ is discontinuous at x = ?

What type of discontinuity?

1. infinite
2. no discontinuity
3. a more "severe type of discontinuity
4. jump
5. removable

Answer 1

There is a discontinuity only at x = 3. It is removable because the limit from either direction is the same sin(1).