Question:

<p><strong>1</strong>: As x \to -1, |x| = -x.</p><p><strong>2</strong>: The expression becomes \lim_{x \to -1} cos 2-cos 2x</p> x2+x .<p><strong>3</strong>: At x = -1, it is a 0/0 form.</p><p><strong>4</strong>: Apply L’Hopital’s Rule: \lim_{x \to -1} 2 sin 2x</p> 2x+1 .<p><strong>5</strong>: Substitute x = -1: 2 sin(-2)</p> -2+1 = -2 sin 2 -1 = 2 sin 2.