How do you find the slant asymptote of #f (x ) = ( 2x^3 + x^2) / (2x^2 - 3x + 3)#?

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Answer 1 · 2016-06-28T04:54:17

#y=x+2#

I must obtain an equation of the type

y=mx+n

First I find m by calculating:

#m=lim_(xrarroo) (2x^3+x^2)/(2x^2-3x+3)*1/x#

#m=lim_(xrarroo) (2x^2+x)/(2x^2-3x+3)#

#m=1#

the I calculate n:

#n=lim_(xrarroo) ((2x^3+x^2)/(2x^2-3x+3)-x)#

#n=lim_(xrarroo) (cancel(2x^3)+x^2cancel(-2x^3)+3x^2-3x)/(2x^2-3x+3)#

#n=lim_(xrarroo) (4x^2-3x)/(2x^2-3x+3)#

#n=2#

so the slant asymptote is

#y=x+2#