Home › Previous year questions › GATE 2019 BT › Question 31GATE 2019 BT – Question 31 Engineering Mathematics · Calculus: Limits, continuity, differentiability, partial derivatives, maxima and minima · 1 mark · Numerical answer
Evaluate $\lim_{x\to8}(x^2-64)/(x-8)$.
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Show answer and explanation Correct answer: 16 to 16
Explanation Factor the numerator as $(x-8)(x+8)$. For x ≠ 8 the ratio equals x+8; the limit is therefore 8+8 = 16. Cancellation is valid in the punctured neighbourhood used to define the limit.
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