GATE | GATE CS 2008 | Question 1

(A) 1
(B) -1
(C) INF
(D) -INF

Answer: (A)

Explanation: $\lim_{x\leftarrow \infty } \frac{x - sin(x)}{x + cos(x)} = \lim_{x\leftarrow 0} \frac{1-\frac{sin(x)}{x}}{1+\frac{cos(x)}{x}} = \frac{1-\lim_{x\leftarrow \infty } \frac{Sin(x)}{x} }{1+\lim_{x\leftarrow \infty } \frac{Cos(x)}{x} }= \frac{1-0}{1+0} = 1$

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