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Limits Continuity And Differentiability

JEE Main 2021 (Online) 20th July Evening Shift

INTEGER+4 / -12021
If \(\mathop {\lim }\limits_{x \to 0} {{\alpha x{e^x} - \beta {{\log }_e}(1 + x) + \gamma {x^2}{e^{ - x}}} \over {x{{\sin }^2}x}} = 10,\alpha ,\beta ,\gamma \in R\), then the value of \(\alpha\) + \(\beta\) + \(\gamma\) is _____________.

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