JEE Mains · Maths · STD 11 - 12. limits
If \(\displaystyle\lim_{x \to 2} \dfrac{\sin(x^3 - 5x^2 + ax + b)}{(\sqrt{x-1} - 1)\log_e(x-1)} = m\), then \(a + b + m\) is equal to :
- A \(5\)
- B \(6\)
- C \(8\)
- D \(10\)
Answer & Solution
Correct Answer
(B) \(6\)
Step-by-step Solution
Detailed explanation
Let \(x - 2 = t\). As \(x \to 2\), \(t \to 0\). The given limit can be written as: \(\lim_{t \to 0} \dfrac{\sin((t+2)^3 - 5(t+2)^2 + a(t+2) + b)}{(\sqrt{t+1} - 1)\log_e(t+1)} = m\) The denominator can be approximated for small \(t\) as:…
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