determinant-

Question Number 194482 by horsebrand11 last updated on 08/Jul/23

\begin{matrix} \underset{―}{\underset{⏟}{⋐}} \end{matrix}

Answered by cortano12 last updated on 08/Jul/23

L = \lim_{x \to 0} [\frac{1}{x^{2}} (\frac{2}{\cos x} + \cos x - 3)]

L = \lim_{x \to 0} (\frac{\cos^{2} x - 3 \cos x + 2}{x^{2} \cos x})

L = \lim_{x \to 0} (\frac{(\cos x - 2) (\cos x - 1)}{x^{2} \cos x})

L = \lim_{x \to 0} (\frac{\cos x - 2}{\cos x}) . \lim_{x \to 0} (\frac{- \sin^{2} x}{x^{2} (\cos x + 1)})

L = - 1 \times (- \frac{1}{2}) = \begin{matrix} \frac{1}{2} \end{matrix}