How do you identify all of the asymptotes of $y = \frac{x^{3} + 5 x^{2} + 3 x + 10}{x^{2} + 2}$ $y = (x^3 + 5x^2 + 3x + 10)/(x^2 + 2)$ ?

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Answer 1 · 2015-09-09T09:04:06

y= x+5

Carry out the long division to write $y = x + 5 + \frac{5 x}{x^{2} + 2}$ $y= x+5+(5x)/(x^2+2)$

This shows that line y= x+5 is its asymptote.

How do you identify all of the asymptotes of y = (x^3 + 5x^2 + 3x + 10)/(x^2 + 2)y=x3+5x2+3x+10x2+2y = (x^3 + 5x^2 + 3x + 10)/(x^2 + 2)?