limx → 4 (sin(x-4))/(x-4) = …

Calculus

GATE CSE 2016 Set 1 · Q3

NAT1 markEasy

Time00:00

$\lim_{x \to 4} \frac{\sin(x-4)}{x-4} = \text{\underline{\hspace{2.2em}}} .$

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Solution

Step-by-step verified solution

Official answer: 1

Calculus

Let $y = x - 4$ . As $x \to 4$ , we have $y \to 0$ .

Substituting $y$ into the limit gives the standard trigonometric limit:

\lim_{y \to 0} \frac{\sin y}{y} = 1

Thus, the answer is 1.

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This Calculus previous year question is Q3 of the GATE CSE 2016 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. 11 of them are 1-mark NAT questions like this one, and it is the only one in GATE CSE 2016 Set 1.

How GATE tests Calculus

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