JEE Mains · Maths · STD 11 - 12. limits
If \(\lim _{x \rightarrow 0} \frac{\alpha x e^{x}-\beta \log _{e}(1+x)+\gamma x^{2} e^{-x}}{x \sin ^{2} x}=10, \alpha, \beta, \gamma \in R\), then the value of \(\alpha+\beta+\gamma\) is \(......\)
- A \(9\)
- B \(6\)
- C \(3\)
- D \(-3\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 0} \frac{\alpha x\left(1+x+\frac{x^{2}}{2}\right)-\beta\left(x-\frac{x^{2}}{2}+\frac{x^{3}}{3}\right)+\gamma x^{2}(1-x)}{x^{3}}\)…
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