The limit p = {\lim}_{x\to \pi } ( {x^{2} + \alphax + 2\pi ^{2}}/{x−\pi + 2 \sin ⁡x}) has a finite value for a real α. The value of α and the corresponding limit p are

Correct Answer is : α = -3π, and p = π

GATE Mechanical Engineering (ME) 2022 Shift 1 Solved Paper

Question : 11 of 65

Marks: +1, -0

The limit

p = {\lim}↙{x→ π } (\;{x^{2}\;+\;αx\;+\;2π\;^{2}}/{x−π\;\;+\;2\ sin\;⁡x})

has a finite value for a real α. The value of α and the corresponding limit p are

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