jee-advanced 2005 Q15

jee-advanced · India · mains Chain Rule Limit Involving Derivative Definition of Composed Functions

15. If $f ( x - y ) = f ( x ) \cdot g ( y ) - f ( y ) \cdot g ( x )$ and $g ( x - y ) = g ( x ) \cdot g ( y ) + f ( x ) \cdot f ( y )$ for all $x$, $y \hat { I } R$. If right hand derivative at $x = 0$ exists for $f ( x )$. Find derivative of $g ( x )$ at $x = 0$.

Let $S$ be the set of all polynomials $P ( x )$ of degree less than or equal to 2 which satisfy the conditions $P ( 1 ) = 1 , P ( 0 ) = 0$ and $P ^ { \prime } ( x ) > 0$ for all $x \in [ 0,1 ]$. Then

15. If $f ( x - y ) = f ( x ) \cdot g ( y ) - f ( y ) \cdot g ( x )$ and $g ( x - y ) = g ( x ) \cdot g ( y ) + f ( x ) \cdot f ( y )$ for all $x$, $y \hat { I } R$. If right hand derivative at $x = 0$ exists for $f ( x )$. Find derivative of $g ( x )$ at $x = 0$.\\

Paper Questions

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