If lim x → 0 (a x² eˣ-b log e (1+x)+c x e⁻ˣ)/(x² sin x)=1, then 16(a²+b²+c²) is equal to _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2024 Mathematics question

JEE Main 2024 · 31 Jan, Evening shift · Q39

JEE Main 202431 Jan, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

\lim _\limits{x \rightarrow 0} \frac{a x^2 e^x-b \log _e(1+x)+c x e^{-x}}{x^2 \sin x}=1

, then

16\left(a^2+b^2+c^2\right)

is equal to ________.

Your answerType your answer. Integers and decimals are accepted.

JEE Main 2024 · 31 Jan, Evening shift · Q39

JEE Main 202431 Jan, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

\lim _\limits{x \rightarrow 0} \frac{a x^2 e^x-b \log _e(1+x)+c x e^{-x}}{x^2 \sin x}=1

, then

16\left(a^2+b^2+c^2\right)

is equal to ________.

Your answerType your answer. Integers and decimals are accepted.