Assertion and reason: continuity

Exercise and reference answers

Questions

1. Reason

   The function must be defined, the limit must exist, and they must match.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   Checking continuity means checking three things agree.

2. Reason

   It is continuous only where the denominator does not vanish.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   A quotient of continuous functions has a restriction.

3. Reason

   Differentiable functions are continuous.

   Verdict

   The assertion is false and the reason is true.

   Assertion

   Continuity implies differentiability.

Explanation