calcu-late-lim-x-pi-2-sin-x-tan-2-x-determinant-

Question Number 195401 by mnjuly1970 last updated on 01/Aug/23

calc \underset{\underset{⇓}{⇓}}{u l a t e}

\lim_{x \to \frac{π}{2}} {(\sin (x))}^{\tan^{2} (x)} = ? \begin{array}{cc}  \end{array}

Answered by MM42 last updated on 01/Aug/23

e^{{l i m}_{x \to \frac{π}{2}} (s i n x - 1) {t a n}^{2} x} = e^{{l i m}_{x \to \frac{π}{2}} \frac{(s i n x - 1) {s i n}^{2} x}{{c o s}^{2} x}}

h o p = e^{{l i m}_{x \to \frac{π}{2}} \frac{\frac{1}{2} s i n 2 x s i n x + (s i n x - 1) s i n 2 x}{- s i n 2 x}}

= e^{{l i m}_{x \to \frac{π}{2}} \frac{\frac{1}{2} s i n x + (s i n x - 1)}{- 1}} = e^{- \frac{1}{2}} = \frac{1}{\sqrt{e}} ✓

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