Math  /  Calculus

Questionf(x)=xsinxx2+11g(x)=xcosxx2limx+flx+(x))\begin{array}{l}f(x)=\frac{x \cdot \sin x}{\sqrt{x^{2}+1}-1} \\ g(x)=\frac{x-\cos x}{x^{2}} \\ \left.\lim _{x \rightarrow+\infty} \operatorname{fl}_{x \rightarrow+\infty}(x)\right)\end{array}

Studdy Solution
بما أن g(x) g(x) يقترب من الصفر عندما يقترب x x من اللانهاية، يمكننا استنتاج أن:
limx+f(g(x))=f(limx+g(x))=f(0)=2 \lim_{x \to +\infty} f(g(x)) = f\left(\lim_{x \to +\infty} g(x)\right) = f(0) = 2
الحل النهائي هو:
limx+f(g(x))=2 \lim_{x \to +\infty} f(g(x)) = 2

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