Assertion and reason

Exercise and reference answers

Questions

1. Reason

   Every differentiable function is continuous, but not the reverse.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   Continuity is a weaker requirement than differentiability.

2. Reason

   The quotient is undefined where the denominator vanishes.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   The quotient rule for continuity carries a condition.

3. Reason

   Continuity compares the limit with the value at that point.

   Verdict

   The assertion is false and the reason is true.

   Assertion

   Continuity at a point guarantees differentiability there.

Explanation