Let f(x) = x⁶ + 2x⁴ + x³ + 2x + 3, x R. Then the natural number n for which lim x → 1 (xⁿf(1) - f(x))/(x - 1) = 44 is _ _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2021 Mathematics question

JEE Main 2021 · 1 Sep, Evening shift · Q37

JEE Main 20211 Sep, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

f(x) = {x^6} + 2{x^4} + {x^3} + 2x + 3

, x

\in

R. Then the natural number n for which

\mathop {\lim }\limits_{x \to 1} {{{x^n}f(1) - f(x)} \over {x - 1}} = 44

is __________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2021 · 1 Sep, Evening shift · Q37

JEE Main 20211 Sep, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

f(x) = {x^6} + 2{x^4} + {x^3} + 2x + 3

, x

\in

R. Then the natural number n for which

\mathop {\lim }\limits_{x \to 1} {{{x^n}f(1) - f(x)} \over {x - 1}} = 44

is __________.

Your answerType your answer. Integers and decimals are accepted.