How to solve the following limit problem?
$$\lim_{x\to\infty} \frac{3x^2+\sin x}{x^2+(\sin x)^2}$$. I have tried the following and arrived at a solution. But not sure if it is correct.
Applying L'Hospital's rule taking derivative thrice I get the following expression:
$$\lim_{x\to\infty} \frac{\cos x}{8\cos 2x} = 0$$
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