Question

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

Answer 1

Answer: 7

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