GATE 2022 PI – Question 45

Engineering Mathematics · Calculus · 2 marks · Numerical answer

Evaluate $\lim_{x\to1}(x^3-3x+2)/(x^3-x^2-x+1)$ to one decimal.

Show answer and explanation

Correct answer: 1.4 to 1.6

Explanation

Factor the numerator as $(x-1)^2(x+2)$ and denominator as $(x-1)^2(x+1)$. Cancel the common factor for x ≠ 1, then evaluate (1+2)/(1+1) = **1.5**.

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