- Consider the limit
For prove that this limit exists and compute the limit.
- For positive real numbers and , Consider the limit
Compute this limit.
- Proof. We use the squeeze theorem to prove existence and compute the value of the limit. Since we have
for all positive integers . Then we have
(We know the second limit from this previous exercise (Section 10.4, Exercise #9).) Therefore, by the squeeze theorem we have
- If then we have and so, using part (a),
On the other hand if then we have and so by part (a) again,