Exams › GATE › Engineering Mathematics

lim_(x→∞) (x − sin x)/(x + cos x) equals

1. 1
2. -1
3. ∞
4. -∞

Correct answer: 1

Solution

As x approaches infinity, the terms involving sine and cosine become negligible compared to the linear terms x in both the numerator and denominator. Thus, the limit simplifies to the ratio of the leading coefficients, which is 1.

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