Let , where denotes the fractional part of . is equal…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let f(x)=sin⁡−1(1−{x})×cos⁡−1(1−{x})2{x}×(1−{x})f(x)=\frac{\sin^{-1}(1-\{x\})\times\cos^{-1}(1-\{x\})}{\sqrt{2\{x\}}\times(1-\{x\})}, where {x}\{x\} denotes the fractional part of xx. L=lim⁡x→0−f(x)L=\lim_{x\to 0^-} f(x) is equal to (a) π2\frac{\pi}{2} (b) π22\frac{\pi}{2\sqrt{2}} (c) π2\frac{\pi}{\sqrt{2}} (d) 2π\sqrt{2}\pi

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