Prove the following

Question:

If $\lim _{x \rightarrow 1} \frac{x^{2}-a x+b}{x-1}=5$, then $a+b$ is equal to :-

  1. $-7$

  2. $-4$

  3. 5

  4. 1


Correct Option: 1

Solution:

$\lim _{x \rightarrow 1} \frac{x^{2}-a x+b}{x-1}=5$

$1-a+b=0$ .............(i)

$2-a=5$ ..............(ii)

$\Rightarrow a+b=-7$

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