Exams › GATE › Engineering Mathematics

\[ \lim_{x\to\infty} \frac{x+\sin x}{x} \] is equal to

1. −∞
2. 0
3. 1
4. ∞

Correct answer: 1

Solution

We have \(\frac{x+\sin x}{x}=1+\frac{\sin x}{x}\). Since \(-1\le \sin x\le 1\), the term \(\frac{\sin x}{x}\to 0\) as \(x\to\infty\). Hence the limit is 1.

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