Let where is fractional part of

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

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 (1) f(0+)=−π2f(0^+) = -\frac{\pi}{2} (2) f(0−)=π42f(0^-) = \frac{\pi}{4\sqrt{2}} (3) f(x)f(x) is continuous at x=0x=0 (4) None of the above

Related theory

Browse the problem library