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Limits Continuity and Differentiability question

2023 · 8 Apr · Shift 2 · Q32

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JEE Main
Mathematics
Limits Continuity and Differentiability
2023 · 8 Apr · Shift 2 · Q32

Limits Continuity and Differentiability question

2023 · 8 Apr · Shift 2 · Q32

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

If

\alpha \gt \beta \gt 0

are the roots of the equation

a x^{2}+b x+1=0

, and

\lim_{x \rightarrow \frac{1}{\alpha}}\left(\frac{1-\cos \left(x^{2}+b x+a\right)}{2(1-\alpha x)^{2}}\right)^{\frac{1}{2}}=\frac{1}{k}\left(\frac{1}{\beta}-\frac{1}{\alpha}\right), \text { then } \mathrm{k} \text { is equal to }

:

A
$2 \beta$
B
$\beta$
C
$\alpha$
D
$2 \alpha$

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