limx→−1 cos⁡2−cos⁡2xx2−|x| is equal to - Infinity Learn by Sri Chaitanya

A
2
B
2 sin 2
C
sin 2
D
0

Solution:

$\begin{array}{l} lim_{x \to - 1} \frac{2 \sin (1 + x) \sin (x - 1)}{x^{2} + x} \\ 2 lim_{x \to - 1} \frac{\sin (x + 1)}{x + 1} \times \frac{\sin (x - 1)}{x} \\ = 2 lim_{x + 1 \to 0} \frac{\sin (x + 1)}{x + 1} lim_{x \to 1} \frac{\sin (x - 1)}{x} \\ = 2 (1) \frac{\sin (- 1 - 1)}{- 1} \\ = 2 \sin 2 \end{array}$

$lim_{x \to - 1} \frac{\cos 2 - \cos 2 x}{x^{2} - | x |} is equal to$

Solution:

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