Question
Write an equation of the slant or nonlinear asymptote. \[ n(x)=\frac{4 x^{3}+5 x^{2}-2 x+2}{x^{2}+4} \] The (Choose one) \( \nabla \) asymptote is \( y=\square \) slant nonlinear
Ask by Williams Byrd. in the United States
Mar 18,2025
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Answer
The slant asymptote is \( y = 4x + 5 \).
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Bonus Knowledge
To find the slant or nonlinear asymptote of the given function \( n(x) = \frac{4x^3 + 5x^2 - 2x + 2}{x^2 + 4} \), perform polynomial long division. Dividing \( 4x^3 + 5x^2 - 2x + 2 \) by \( x^2 + 4 \) gives us a result of \( 4x + 5 \), which means the equation of the slant asymptote is \( y = 4x + 5 \). So, the slant asymptote is \( y = 4x + 5 \).