3.5-bo'lim : Trig funksiyalarining hosilalari
1. \(\displaystyle \mathop {\lim }\limits_{z \to \,0} \frac{{\sin \left( {10z} \right)}}{z}\) ni baholang.
Yechim
Biz qilishimiz kerak bo'lgan yagona narsa ushbu bo'limdagi qaydlardagi faktlardan foydalanishimizga imkon berish uchun buni sozlashdir.
\[\mathop {\lim }\limits_{z \to \,0} \frac{{\sin \left( {10z} \right)}}{z} = \mathop {\lim }\limits_{z \to \,0} \frac{{10\sin \left( {10z} \right)}}{{10z}} = 10\mathop {\lim }\limits_{z \to \,0} \frac{{\sin \left( {10z} \right)}}{{10z}} = 10\left( 1 \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{10}}\]