The value of limx → ∞ (1 + x2)e-x is A) 0 B) (1)/(2) C) 1 D) ∞

Official answer: A) 0. Explanation: We need to evaluate the limit: limx → ∞ (1 + x2)e-x = limx → ∞ (1 + x2)/(ex) This is an indeterminate form of type (∞)/(∞). Applying L'Hôpital's Rule: limx → ∞ (d)/(dx)(1 + x2)(d)/(dx)(ex) = limx → ∞ (2x)/(ex) Applying L'Hôpital's Rule a second time: limx → ∞ (d)/(dx)(2x)(d)/(dx)(ex) = limx → ∞ (2)/(ex) = 0 Thus, the correct option is (A).

Calculus

GATE CSE 2015 Set 3 · Q9

MCQ1 markEasy

Time00:00

The value of $\lim_{x \to \infty} (1 + x^2)e^{-x}$ is

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Official answer: A) 0

Calculus

We need to evaluate the limit:

\lim_{x \to \infty} (1 + x^2)e^{-x} = \lim_{x \to \infty} \frac{1 + x^2}{e^x}

This is an indeterminate form of type $\frac{\infty}{\infty}$ . Applying L'Hôpital's Rule:

\lim_{x \to \infty} \frac{\frac{d}{dx}(1 + x^2)}{\frac{d}{dx}(e^x)} = \lim_{x \to \infty} \frac{2x}{e^x}

Applying L'Hôpital's Rule a second time:

\lim_{x \to \infty} \frac{\frac{d}{dx}(2x)}{\frac{d}{dx}(e^x)} = \lim_{x \to \infty} \frac{2}{e^x} = 0

Thus, the correct option is (A).

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This Calculus previous year question is Q9 of the GATE CSE 2015 Set 3 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. 14 of them are 1-mark MCQs like this one, and GATE CSE 2015 Set 3 has 3.

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