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$If f (x) = \int \frac{x + \sin x}{x + \cos x} d x, then lim_{x \to \infty} f (x) =$

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Correct option is B

We have f(x)=∫x+sinxx+cosxdx⇒ f(x)=x+sinxx+cosx⇒ limx→∞ f(x)=limx→∞1+sinxx1+cosxx=1+01+0=1 ∴limx→∞1x=0 and sinx≤1,cosx≤1 for all xHence (2) is the correct answer.

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If f(x)=∫x+sin⁡xx+cos⁡xdx, then limx→∞ f(x)=

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$If f (x) = \int \frac{x + \sin x}{x + \cos x} d x, then lim_{x \to \infty} f (x) =$