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When in the horizontal asymptote 0?
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when the degree of the polynomial on top is less than the degree of the polynomial on bottom
Example, x2/x
\[\frac{x}{x^2}\] \[\frac{x/x}{x^2/x}\] \[\lim_{x->\infty}\ \frac{1}{x}=0\]
that was odd lol
dont we normally divide out the bottom?
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\[\frac{x}{x^2}\] \[\frac{x/x^2}{x^2/x^2}\] \[\frac{1/x}{1}=\frac{1}{x}\]
gj lol
when \[\lim_{x\to\infty}f(x)=0\] or \[\lim_{x\to-\infty}f(x)=0\] f(x) need not be a rational function
for example \[\lim_{x\rightarrow\infty}\frac{\sin(x)}{x}\]
nope it doesn't have to be rational
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