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Limits Continuity and Differentiability question

2024 · 8 Apr · Shift 2 · Q58

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JEE Main
Mathematics
Limits Continuity and Differentiability
2024 · 8 Apr · Shift 2 · Q58

Limits Continuity and Differentiability question

2024 · 8 Apr · Shift 2 · Q58

JEE MainMathematicsLimits Continuity and DifferentiabilityNumerical+4 / −1

If

\alpha=\lim_{x \rightarrow 0^{+}}\left(\frac{\mathrm{e}^{\sqrt{\tan x}}-\mathrm{e}^{\sqrt{x}}}{\sqrt{\tan x}-\sqrt{x}}\right)

and

\beta=\lim_{x \rightarrow 0}(1+\sin x)^{\frac{1}{2} \cot x}

are the roots of the quadratic equation

\mathrm{a} x^2+\mathrm{b} x-\sqrt{\mathrm{e}}=0

, then

12 \log _{\mathrm{e}}(\mathrm{a}+\mathrm{b})

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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