A) \[-1\]
B) \[0\]
C) \[\frac{1}{2}\]
D) \[1\]
Correct Answer: D
Solution :
Key Idea: \[\underset{x\to \infty }{\mathop{\lim }}\,\frac{\sin x}{x}=0,\,\,\underset{x\to \infty }{\mathop{\lim }}\,\frac{\cos x}{x}=0\] Let \[A=\underset{x\to \infty }{\mathop{\lim }}\,\sqrt{\frac{x-\sin x}{x+{{\cos }^{2}}x}}\] \[\Rightarrow \] \[A=\underset{x\to \infty }{\mathop{\lim }}\,\sqrt{\frac{1-\frac{\sin x}{x}}{1+\frac{{{\cos }^{2}}x}{x}}}\] \[\Rightarrow \] \[A=\sqrt{\frac{1-0}{1+0}}=1\]
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