If α > β > 0 are the roots of the equation a x²+b x+1=0, and lim x → 1/(α) ((1- cos (x²+b x+a))/(2(1-α x)²))^(1/2)=1/k(1/(β)-1/(α)), then k is equal to:

Limit, Continuity and Differentiability: JEE Main 2023 Mathematics question

JEE Main 2023 · 8 Apr, Evening shift · Q4299

JEE Main 20238 Apr, Evening shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

\alpha > \beta > 0

are the roots of the equation

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

, and

\lim_\limits{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 }

JEE Main 2023 · 8 Apr, Evening shift · Q4299

JEE Main 20238 Apr, Evening shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

\alpha > \beta > 0

are the roots of the equation

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

, and

\lim_\limits{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 }