sin2x−x2 cos2x | ||
Oblicz limx−>0 | ||
x2 sin2x |
sin2x−x2cos2x | (1+x2)sin(2x)−2xcos2x | |||
limx→0 | = H = limx→0 | = H | ||
x4 | 4x3 |
4xsin(2x)+2(1+x2)cos(2x)−2cos2x | ||
= limx→0 | = H = | |
12x2 |
(2−4x2)sin(2x)+12xcos(2x) | 1 | 1 | 2 | |||||
= limx→0 | = | + | = | |||||
24x | 6 | 2 | 3 |
sin2x−x2cos2x | sin2x−x2cos2x | ||
zamiast | |||
x4 | x2sin2x |
sin2x−x2cos2x | sin2x−x2cos2x | x2 | 2 | |||
= | → | |||||
x2sin2x | x4 | sin2x | 3 |
sinx | ||
ponieważ limx→0 | = 1 | |
x |