Write an equation of the slant or nonlinear asymptote. \( m(x)=\frac{36 x^{4}+20 x^{2}-15}{4 x^{2}+4} \) The \( \begin{array}{l}\text { (Choose one) } \\ \text { nonlinear } \\ \text { slant }\end{array} \)
Solución de inteligencia artificial de Upstudy
Responder
Solución

¡Inicia sesión para desbloquear respuestas gratis!
Una plataforma de aprendizaje en la que confían millones de estudiantes y profesores reales.

Respondido por UpStudy AI y revisado por un tutor profesional
Beyond the Answer
To find the slant or nonlinear asymptote of the function \( m(x)=\frac{36 x^{4}+20 x^{2}-15}{4 x^{2}+4} \), you need to perform polynomial long division because the degree of the numerator is greater than the degree of the denominator. Dividing, you'll find that \( m(x) \) can be approximated by \( 9x^{2} + \frac{20x^{2} - 15 - 36x^{4}}{4x^{2} + 4} \). As \( x \) tends to infinity, the term \(\frac{20x^{2} - 15 - 36x^{4}}{4x^{2} + 4}\) approaches zero, leading to the slant asymptote equation \( y = 9x^{2} \). To summarize, the slant asymptote for the given function is \( y = 9x^{2} \). This means that as the value of \( x \) increases or decreases without bound, the graph of \( m(x) \) will approach the curve described by \( y = 9x^{2} \). So, when you plot the function, keep an eye on how closely it hugs that parabola at both ends!
