MHB What is the Slant Asymptote of $\dfrac{4x^3-10x^2-11x-1}{x^2-3x}$?

[karush]

$\tiny{s8.3.6.46}$

Find the Slant asymptote
$y=\dfrac{4x^3-10x^2-11x-1}{x^2-3x}$

Ok the last time I did a slant asymptote was decades ago in Algrebra but this is a calculus problem

the example started with this $\displaystyle\lim_{x \to \infty}[f(x)-(mx+b)]=0$

long division returns $4x+2+\dfrac{-5x-1}{x^2-3x}$ and a desmos graph looks like y=x+3 is sort of close to the SA

so far.. anyway.. but next?

 

[HOI]

$\tiny{s8.3.6.46}$

Find the Slant asymptote
$y=\dfrac{4x^3-10x^2-11x-1}{x^2-3x}$

Ok the last time I did a slant asymptote was decades ago in Algrebra but this is a calculus problem

the example started with this $\displaystyle\lim_{x \to \infty}[f(x)-(mx+b)]=0$

long division returns $4x+2+\dfrac{-5x-1}{x^2-3x}$ and a desmos graph looks like y=x+3 is sort of close to the SA

For very large x, that fraction will be very small so I would think the graph would be much closer to $4x+ 2$!

so far.. anyway.. but next?

 

[karush]

i should of seen that

 

[karush]

https://dl.orangedox.com/GXEVNm73NxaGC9F7Cy
38 pages of calculus
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