Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems 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\})} f ( x ) = 2 { x } × ( 1 − { x }) s i n − 1 ( 1 − { x }) × c o s − 1 ( 1 − { x })
Mathematics
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\})} f ( x ) = 2 { x } × ( 1 − { x }) s i n − 1 ( 1 − { x }) × c o s − 1 ( 1 − { x }) { x } \{x\} { x } x x x L = lim x → 0 − f ( x ) L=\lim_{x\to 0^-} f(x) L = lim x → 0 − f ( x ) π 2 \frac{\pi}{2} 2 π π 2 2 \frac{\pi}{2\sqrt{2}} 2 2 π π 2 \frac{\pi}{\sqrt{2}} 2 π 2 π \sqrt{2}\pi 2 π Browse the problem library