| |||||||||||
lim | |||||||||||
| 1−2cosx |
| π | ||
x→ | ||
| 3 |
| cos(x−π/3) | 1 | |||
H = limx→π/3 | = | |||
| 2sinx | √3 |
| sint | t | |||
limt→0 | * | = | ||
| t | 1−2cos(t+π/3) |
| sint | t | |||
= limt→0 | * | = | ||
| t | 1−cost+√3sint |
| sint | 1 | |||
= limt→0 | * | |||
| t | (1−cost)/t+√3sint/t |
| sint | 1 | |||
= limt→0 | * | |||
| t | (t/2)sin2(t/2)/(t/2)2+√3sint/t |
| sinx | ||
teraz korzystając z granicy limx→0 | ||
| x |
| 1 | 1 | |||
granica = 1* | = | |||
| 0*1+√3 | √3 |