| tgx − sinx | 0 | ||
, gdy za x podstawie 0 bedzie | czyli symbol nieoznaczony | ||
| sin3x | 0 |
| a | ||
limx → 0 ( | ) | |
| b |
| sinx | sinx − sinxcosx | 1 − cosx | sinx | |||||
a= | −sinx = | = sinx( | = | * | ||||
| cosx | cos | cosx | cosx |
| 1−cosx | 1 | |||
(1−cosx)= tgx * | *x2 = tgx * | |||
| x2 | 2 |
| 1−cosx | 1 | ||
= | |||
| x2 | 2 |
| sin3x | ||
b= | *x=1*x | |
| x |
| 1 | ||||||||||||||
= | dobrze? | ||||||||||||||
| x | 2 |
| tgx−sinx | sinx( 1/cosx −1) | 1−cosx | |||
= | = | = | |||
| sin3 x | sin3 x | cosx(1−cos2 x) |
| 1−cosx | 1 | 1 | |||
= | → | gdy x→0 | |||
| cosx(1−cosx)(1+cosx) | cosx(1+cosx) | 2 |
