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GATE 2024 PI – Question 32

Engineering Mathematics · Calculus · 1 mark · Numerical answer

$\lim_{x\to1}(x^2-2ax+b)/(x-1)=8$. Find a − b (integer).

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Correct answer: 4 to 4

Explanation

For a finite limit, numerator at x = 1 must vanish: $1-2a+b=0$. Its derivative there is 2−2a, which equals the stated limit 8. Hence a = −3 and b = 2a−1 = −7, giving **a−b = 4**.

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