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Limits Continuity and Differentiability question

2022 · 26 Jul · Shift 2 · Q25

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JEE Main
Mathematics
Limits Continuity and Differentiability
2022 · 26 Jul · Shift 2 · Q25

Limits Continuity and Differentiability question

2022 · 26 Jul · Shift 2 · Q25

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

\beta=\mathop {\lim }\limits_{x \to 0} \frac{\alpha x-\left(e^{3 x}-1\right)}{\alpha x\left(e^{3 x}-1\right)}

for some

\alpha \in \mathbb{R}

. Then the value of

\alpha+\beta

is :

A
$\frac{14}{5}$
B
$\frac{3}{2}$
C
$\frac{5}{2}$
D
$\frac{7}{2}$

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