If $\alpha $ is positive root of the equation, p(x) = x2 - x - 2 = 0, then $\mathop {\lim }\limits_{x \to {\alpha ^ + }} {{\sqrt {1 - \cos \left( {p\left( x \right)} \right)} } \over {x + \alpha - 4}}$ is equal to :

Question

If $\alpha $ is positive root of the equation, p(x) = x² - x - 2 = 0, then

$\mathop {\lim }\limits_{x \to {\alpha ^ + }} {{\sqrt {1 - \cos \left( {p\left( x \right)} \right)} } \over {x + \alpha - 4}}$ is equal to :

${1 \over \sqrt2}$

${1 \over 2}$

${3 \over \sqrt2}$

${3 \over 2}$

Solution

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