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We are asked to solve the equation: \[ \lim_{x\rightarrow\infty}\frac{x(1+a\cos x)-b\sin x}{x^3}=1 \] ### Step 1: Rewrite the equation for clarity The given equation is: \[ \lim_{x\rightarrow\infty}\frac{x(1+a\cos x)-b\sin x}{x^3}=1 \] We need to analyze the behavior of this expression as \(x\) approaches infinity. Let’s expand it: \[ \frac{x(1+a\cos x)-b\sin x}{x^3} = \frac{x + ax\cos x - ______ ______ ________ ____ _________ ________ ____ ______ ____ _____ __________.
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