JEE Mains · Maths · STD 11 - 12. limits
If \(\lim _{x \rightarrow 0} \frac{a x^2 e^x-b \log _e(1+x)+c x e^{-x}}{x^2 \sin x}=1\), then \(16\left(a^2+b^2+c^2\right)\) is equal to ...........
- A \(80\)
- B \(85\)
- C \(81\)
- D \(70\)
Answer & Solution
Correct Answer
(C) \(81\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0} \frac{a^2\left(1+x+\frac{x^2}{2 !}+\frac{x^3}{3 !}+\ldots . .\right)-b\left(x-\frac{x^2}{2}+\frac{x^3}{3}-\ldots \ldots . .\right)\\+c x\left(1-x+\frac{x^2}{x !}-\frac{x^3}{3 !}+\ldots \ldots . .\right)}{x^3 \cdot \frac{\sin x}{x}} \)…
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