Gönderen Konu: Birim Çemberde Trigonometrik Limit  (Okunma sayısı 49 defa)

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Birim Çemberde Trigonometrik Limit
« : Şubat 12, 2019, 11:20:27 ÖS »

https://i.ibb.co/D9s9wjd/limit7.png
https://scontent-vie1-1.xx.fbcdn.net/v/t1.0-9/52039670_244011623206756_393290086575243264_n.jpg?_nc_cat=107&_nc_ht=scontent-vie1-1.xx&oh=fc5d63889ee8ed3bd3bd403f97fa1d52&oe=5CED778C
https://www.facebook.com/photo.php?fbid=244011613206757&set=gm.2579326572082692&type=3&theater&ifg=1

sinx = |AD| / 1 ⇒ |AD| = sinx

tanx = |BC| / 1 ⇒ |BC| = tanx

cosx = |AO| / 1 ⇒ |AO| = cosx

|AB| = 1 - |AO| = 1 - cosx

lim x → 0+ |AD|·|BC| / |AB| = lim x → 0+ (sinx)·(tanx) / (1 - cosx) =

lim x → 0+ 2·[ sin(x / 2) ]·[ cos(x / 2) ]·tan(x) / { 1 - 1 + 2[ sin(x / 2) ]2 } =

lim x → 0+ [ cot(x / 2) ]·tan(x) = lim x → 0+ [ cot(x / 2) ]·2·[ tan(x / 2) ] / { 1 - [ tan(x / 2) ]2 } =

2lim x → 0+ 1 / { 1 - [ tan(x / 2) ]2 } = 2[ 1 / (1 - 0) ] = 2