| 3 | ||
jak policzyć taki rodzaj granic , np. lim n( cos | −1) | |
| √n |
| A | ||||||||
A*B= | i de Hospital | |||||||
|
| 3 | 9 | |||
Użyjemy podstawienia u = | , czyli n = | . | ||
| √n | u2 |
| 3 | 9 | (cosu−1) | cosu+1 | |||||
an = n(cos | − 1) = | (cosu−1) = 9* | * | = | ||||
| √n | u2 | u2 | cosu+1 |
| 9 | cos2u−1 | 9 | −sin2u | |||||
= | * | = | * | = | ||||
| cosu+1 | u2 | cosu+1 | u2 |
| 9 | sinu | sinu | ||||
= − | * | * | = bu | |||
| cosu+1 | u | u |
| 9 | ||
limn→∞ an = limu→0+ bu = − | . | |
| 2 |