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What are the asymptotes and removable discontinuities, if any, of #f(x)=(2x^3-x+1)/(x^2+1) #?

1 Answer

Jul 7, 2018

Asymptote #y=2x#

Explanation:

#x^2+1ne 0# so no vertical asymptotes.
The only Asymptote is #y=2x#
We get

#(2x^3-x+1)/(x^2+1)-2x=(1-2x)/(x^2+1)#
and we have
#lim_(xto pm infty)(1-3x)/(x^2+1)=0#

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