| sin nx | ||
lim | ||
| sin mx |
| arcsinx | ||
1) lim x→0 ctgx*arcsinx= lim x→0 cosx * | = | |
| sinx |
| arcsinx | x | |||
= cos0 * lim x→0 | * limx→0 | = | arcsinx=t, to x=sint , t →0 | = | ||
| x | sinx |
| t | 1 | |||||||||
= 1 * lim t→0 | * lim x→0 | = 1 * 1= 1 ; | ||||||||
| sint |
|
| sin nx | sin nx | |||
2) limx→π | =limx−π→0 | = | x−π=t , to x=π+t i t→0 | = | ||
| sin mx | sin mx |
| sin n(π+t) | sin (nπ+nt) | |||
= lim t→0 | = lim t→0 | = | ||
| sin m(π+t) | sin (mπ+mt) |
| sin (2nπ2+nt) | ||
= lim t→0 | = | |
| sin (2mπ2+mt) |
| (−1)n sin nt | ||
= lim t→0 | = | |
| (−1)m sin mt |
| n | sin nt | mt | n | |||||
= (−1)n−m lim t→0 | * | * | = (−1)n−m * | * 1 * 1= | ||||
| m | nt | sin mt | m |
| n | ||
= (−1)n−m | − szukana granica , gdzie n,m∊N . ...  | |
| m |