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Limits Continuity and Differentiability question

2021 · 20 Jul · Shift 2 · Q45
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  5. /2021 · 20 Jul · Shift 2 · Q45

Limits Continuity and Differentiability question

2021 · 20 Jul · Shift 2 · Q45

JEE MainMathematicsLimits Continuity and DifferentiabilityNumerical+4 / −1
If lim⁡x→0αxex−βlog⁡e(1+x)+γx2e−xxsin⁡2x=10,α,β,γ∈R\mathop {\lim }\limits_{x \to 0} {{\alpha x{e^x} - \beta {{\log }_e}(1 + x) + \gamma {x^2}{e^{ - x}}} \over {x{{\sin }^2}x}} = 10,\alpha ,\beta ,\gamma \in Rx→0lim​xsin2xαxex−βloge​(1+x)+γx2e−x​=10,α,β,γ∈R, then the value of α\alphaα+β\betaβ+γ\gammaγ is ‾\underline{\hspace{2cm}}​.
Numerical answer
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