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  4. If displaystyle limx→1 (x2 -ax+b/x-1) = 5 , then a + b is equal to :-

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Q. If $\displaystyle\lim_{x\to1} \frac{x^{2} -ax+b}{x-1} = 5 $ , then a + b is equal to :-

JEE MainJEE Main 2019Limits and Derivatives

Solution:

$\lim_{x\to1} \frac{x^{2} -ax+b}{x-1} = 5 $
$1 - a + b = 0$ ...(i)
$2 - a = 5$ ...(ii)
$\Rightarrow a + b = - 7$.