<p>If A = limx→0
sin−1(sin x)
cos−1(cos x) and B = limx→0
[|x|]
x , then:</p>
Step-by-Step Solution
Key Concept: General
<p><strong>1</strong>: For x near 0, sin-1(sin x) = x.</p><p><strong>2</strong>: For x near 0, cos-1(cos x) = |x|.</p><p><strong>3</strong>: A = \lim_{x \to 0} x</p> |x|. LHL is -1, RHL is 1. Limit D.N.E.<p><strong>4</strong>: For B, as x \to 0, |x| is a very small positive number, so [|x|] = [01] = 0.</p><p><strong>5</strong>: B = \lim_{x \to 0} 0</p> x = 0.
Correct Answer: (B, C)