Continuity — true or false?

Exercise and reference answers

Questions

1. Statement is true

   Yes

   Statement

   If f is differentiable at a, then f is continuous at a.

2. Statement is true

   No

   Statement

   Every continuous function is differentiable.

3. Statement is true

   Yes

   Statement

   f(x) = |x| is continuous but not differentiable at x = 0.

4. Statement is true

   Yes

   Statement

   A removable discontinuity can be fixed by redefining one point.