2.8-bo'lim : Infinity chegaralari, II qism
12. \(\displaystyle \mathop {\lim }\limits_{w \to \,\infty } {\tan ^{ - 1}}\left( {\frac{{3{w^2} - 9{w^4}}}{{4w - {w^3}}}} \right)\) ni baholang.
Yechim
Avval e'tibor bering,
\[\mathop {\lim }\limits_{w \to \,\infty } \frac{{3{w^2} - 9{w^4}}}{{4w - {w^3}}} = \infty \]Agar siz ushbu cheklovga ishonchingiz komil bo'lmasa, avvalgi bo'limga qaytib, ushbu turdagi limitlarni amalga oshirishingiz mumkinligiga ishonch hosil qilish uchun u erdagi ba'zi misollar bilan ishlashingiz kerak.
Endi eslash 7-misol Ushbu bo'limdan biz bilamizki, argument chegarada cheksiz bo'lganligi sababli javob:
\[\mathop {\lim }\limits_{w \to \,\infty } {\tan ^{ - 1}}\left( {\frac{{3{w^2} - 9{w^4}}}{{4w - {w^3}}}} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{\pi }{2}}}\]