JEE Main 2003Annual, Paper 1MathematicsMediumLimit, Continuity and Differentiability420× since 2002If f(x)=xn,f\left( x \right) = {x^n},f(x)=xn, then the value of f(1)−f′(1)1!+f′′(1)2!−f′′′(1)3!+..........(−1)nfn(1)n!f\left( 1 \right) - {{f'\left( 1 \right)} \over {1!}} + {{f''\left( 1 \right)} \over {2!}} - {{f'''\left( 1 \right)} \over {3!}} + ..........{{{{\left( { - 1} \right)}^n}{f^n}\left( 1 \right)} \over {n!}}f(1)−1!f′(1)+2!f′′(1)−3!f′′′(1)+..........n!(−1)nfn(1) isAOption A. 111BOption B. 2n{{2^n}}2nCOption C. 2n−1{{2^n} - 1}2n−1DOption D. 000CheckSkip · show solution
