JEE Main 2021 (Online) 1st September Evening ShiftQuestion 1
Let $f(x)=x^{6}+2x^{4}+x^{3}+2x+3$, $x\in R$. Then the natural number $n$ for which $\lim_{x\to1}\frac{x^{n}f(1)-f(x)}{x-1}=44$ is ______.
Limits & Continuity
Answer$7$
Solution
$f(1)=9$ and the limit is $\frac{d}{dx}(9x^n-f(x))|_{x=1}=9n-f'(1)=9n-19$. $9n-19=44$ gives $n=7$.