the slant asymptote of f(x) = (x^3 - 2x^2 + x - 4)/(x^2 + 1) is y = x - 2. please select the best answer…
the slant asymptote of f(x) = (x^3 - 2x^2 + x - 4)/(x^2 + 1) is y = x - 2. please select the best answer from the choices provided o t o f
Answer
Explanation:
Step1: Perform polynomial long - division
Divide $x^{3}-2x^{2}+x - 4$ by $x^{2}+1$. We know that $\frac{x^{3}-2x^{2}+x - 4}{x^{2}+1}=\frac{x^{3}+x-2x^{2}-x - 4}{x^{2}+1}=x - 2+\frac{-x - 2}{x^{2}+1}$.
Step2: Analyze the slant asymptote
As $x\to\pm\infty$, the term $\frac{-x - 2}{x^{2}+1}\to0$. So the slant asymptote of $y = f(x)$ is $y=x - 2$.
Answer:
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