Let f(x)=(π2−sin⁡−1(1−{x}2))⋅sin⁡−1(1−{x})2({x}−{x}3),x≠0,f(x) = \frac{\left( \frac{\pi}{2} - \sin^{-1}(1-\{x\}^2) \right) \cdot \sin^{-1}(1-\{x\})}{\sqrt{2(\{x\}-\{x\}^3)}}, x \neq 0,…

Mathematics

Problem

Let f(x)=(π2−sin⁡−1(1−{x}2))⋅sin⁡−1(1−{x})2({x}−{x}3),x≠0,f(x) = \frac{\left( \frac{\pi}{2} - \sin^{-1}(1-\{x\}^2) \right) \cdot \sin^{-1}(1-\{x\})}{\sqrt{2(\{x\}-\{x\}^3)}}, x \neq 0, where {.}\{.\} is fractional part of xx , then a. f(0+)=−π2f(0^+) = -\frac{\pi}{2} b. f(0−)=π42f(0^-) = \frac{\pi}{4\sqrt{2}} c. f(x)f(x) is continuous at x=0x=0 d. None of the above

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