lim x→0 cos^−1(1−x^2)sin^−1(1−{x}) / {x}−{x}^3, where { } is fractional part function.

Question

\(\lim\limits_{x \to 0} \frac{\cos^{-1} (1 - {x}^2) \sin^{-1}(1 - \{x\})}{\{x\} - \{x\}^3}\), where { } is fractional part function.

If L.H.L = L and R.H.L = R, then the correct relation between L and R is

(1) √2R = 4L

(2) √2L = 4R

(3) R = L

(4) R = 2L

Answer 1

Correct option is (1) √2R = 4L