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| Slant Asymptote |
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| Find all asymptotes of y=(x^2-4)/(x+1) x+1/x^2-4\x-1 +++ x^2+x --------- - ++++++ -x-4 ++++++ -x+1 ----------- - ++++++++ -5 y=(x^2-4)/(x+1)=x-1 - 5/(x+1) this means that this function has slant asymptote y=x-1 Vertical asymptote : its denominator approaches to 0 x+1 approaches 0 x approaches -1 x=-1 is vertical asymptote Horizontal asymptotes : x --> ~ y=lim (x^2-4)/(x+1) as x --> ~ y=lim (x^2/x-4/x)/(x/x+1/x) as x--> ~ y=lim (x-4/x)/(1+1/x) as x--> ~ y=~ means there is no horizontal asymptote |
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