MHT CET · Maths · Limits
If \(\lim _{x \rightarrow 1} \frac{x^2-a x+b}{(x-1)}=5\), then \((a+b)\) is equal to
- A \(-3\)
- B \(-4\)
- C \(7\)
- D \(-7\)
Answer & Solution
Correct Answer
(D) \(-7\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow 1} \frac{x^2-a x+b}{x-1}=5\)
Applying \(\Rightarrow a=-3\) Hospital's rule
\(\begin{aligned} & \Rightarrow 2 \times 1-a=5 \\ & \Rightarrow a=-3\end{aligned}\)
from (1) \(b=-4\)
\(\Rightarrow a+b=-7\)
Applying \(\Rightarrow a=-3\) Hospital's rule
\(\begin{aligned} & \Rightarrow 2 \times 1-a=5 \\ & \Rightarrow a=-3\end{aligned}\)
from (1) \(b=-4\)
\(\Rightarrow a+b=-7\)
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