| 3 | ||
lim (2x+3) sin | ||
| 5x |
| sin(3/5x) | 5x | |||
= lim | * | *(2x+3) = [1*∞] = +∞ | ||
| 3/5x | 3 |
| 3 | ||
limx → ∞ (2x + 3)sin( | ) = | |
| 5x |
| 3 | 3 | |||
limx → ∞ 2x • sin( | ) + limx → ∞ 3sin( | ) = | ||
| 5x | 5x |
| 3 | 3 | |||||||||||||
limx → ∞ 2 • | • | + limx → ∞ 3sin( | ) = | ||||||||||||
| 5 | 5x |
| 3 | 6 | |||
2 • 1 • | + 0 = | |||
| 5 | 5 |
| 1 | ||
Jeżeli tego nie widać, niech | = u, jeżeli x → ∞ to u → 0. | |
| x |
| 2 | 3 | |||
limu → 0 ( | + 3)sin( | u) = | ||
| u | 5 |
| 2 | 3 | 3 | ||||
limu → 0 | • sin( | u) + limu → 0 3sin( | u) = | |||
| u | 5 | 5 |
| 3 | 3 | |||||||||||||
limu → 0 2 • | • | + limu → 0 3sin( | u) = | ||||||||||||
| 5 | 5 |
| 3 | 6 | |||
2 • 1 • | + 0 = | |||
| 5 | 5 |
| sin(3/5x) | 3 | |||
= lim | * | *(2x + 3) | ||
| 3/5x | 5x |
