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

If $\lim _{x \rightarrow 1} \frac{x^2-a x+b}{(x-1)}=5$, then $(a+b)$ is equal to
  1. $-3$
  2. $-4$
  3. $7$
  4. $-7$

Solution

Applying $\Rightarrow a=-3$ Hospital's rule $\begin{aligned} & \Rightarrow 2 \times 1-a=5 \\ & \Rightarrow a=-3\end{aligned}$ from (1) $b=-4$ $\Rightarrow a+b=-7$

Asked in: MHT CET 2022 (06 Aug Shift 2)

Practice more Limits questions on Aicharya