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  4. If lim limitsx→1 (x2 - ax + b/x - 1) = 5 and a + b is equal to -c, then value of c is

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Q. If $\lim\limits_{x\to1} \frac{x^2 - ax + b}{x - 1} = 5$ and $ a + b$ is equal to $-c$, then value of $c$ is

Limits and Derivatives

Solution:

$\lim\limits_{x\to1} \frac{x^2 - ax + b}{x - 1} = 5$
$\because $ limit is finite.
$\therefore 1 - a + b = 0$
$ \Rightarrow \lim\limits_{x\to1} \frac{2x - a}{1} = 5 (\frac{0}{0}$ form)(By L Hospital's rule)
$\Rightarrow 2 - a = 5 \Rightarrow a = -3 $ and $b = -4$
Then $ a + b = -3 - 4 = -7$
$\Rightarrow -c = -7$
$\Rightarrow c = 7$