Question-106072

Question Number 106072 by bemath last updated on 02/Aug/20

Answered by bobhans last updated on 02/Aug/20

\lim_{x \to π / 2} \frac{\sqrt{2 \sin^{2} x + 3 \sin x + 4}}{\cot^{2} x} =

set x = \frac{π}{2} + h \Rightarrow \lim_{h \to 0} \frac{3}{\cot^{2} (h + \frac{π}{2})} =

\lim_{h \to 0} \frac{3}{\tan^{2} h} = \lim_{h \to 0} \frac{{3 h}^{2}}{\tan^{2} h} \times \lim_{h \to 0} \frac{1}{h^{2}} = \infty

Answered by Dwaipayan Shikari last updated on 02/Aug/20

\sqrt{2 {s i n}^{2} x + 3 s i n x + 4}

\sqrt{3} ⩽ \sqrt{2 {s i n}^{2} x + 3 s i n x + 4} ⩽ 3

\sqrt{2 {s i n}^{2} x + 3 s i n x + 4} \neq 0

a s {t a n}^{2} x \to \infty

t h e w h o l e f u n c t i o n r e a c h e s t o i n f i n i t y