The value of limx → 1 (x7 - 2x5 + 1)/(x3 - 3x2 + 2) A) is 0 B) is -1 C) is 1 D) does not exist

Calculus

GATE CSE 2017 Set 1 · Q28

MCQ2 marksEasy

Time00:00

The value of $\lim_{x \to 1} \frac{x^7 - 2x^5 + 1}{x^3 - 3x^2 + 2}$

Select one answerSingle correct

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Solution

Step-by-step verified solution

Official answer: C) is 1

Calculus

Evaluating the limit at $x = 1$ gives the indeterminate form $\frac{0}{0}$ :

\text{Numerator at } x=1: 1^7 - 2(1)^5 + 1 = 0

\text{Denominator at } x=1: 1^3 - 3(1)^2 + 2 = 0

Applying L'Hôpital's Rule by differentiating the numerator and denominator with respect to $x$ :

\lim_{x \to 1} \frac{\frac{d}{dx}(x^7 - 2x^5 + 1)}{\frac{d}{dx}(x^3 - 3x^2 + 2)} = \lim_{x \to 1} \frac{7x^6 - 10x^4}{3x^2 - 6x}

Substitute $x = 1$ :

\frac{7(1)^6 - 10(1)^4}{3(1)^2 - 6(1)} = \frac{7 - 10}{3 - 6} = \frac{-3}{-3} = 1

Hence, the correct option is (C).

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This Calculus previous year question is Q28 of the GATE CSE 2017 Set 1 paper. Find more GATE CSE PYQs on Calculus in Engineering Mathematics, or browse all GATE CSE PYQs.

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Calculus in GATE CSE

Calculus has 40 GATE CSE PYQs across 25 papers from 2011 to 2026. 8 of them are 2-mark MCQs like this one, and it is the only one in GATE CSE 2017 Set 1.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.