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| Fraction Function |
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| Find all the asymptotes of y=(x^2+1)/(x^2-4) Solution : Vertical asymptotes to be reached when its denominator of right side approaches 0 x^2-4 approahes 0 (x-2)(x+2) approaches 0 means x-2 approaches 0 or x approaches 2 and x+2 approaches 0 or x approaches -2 thus x=2 and x=-2 are vertical asymptotes Horizontal asymptotes reached when x approaches to infinity y=lim (x^2+1)/(x^2-4) as x--> ~ (infinity) y=lim (x^2/x^2+1/x^2)/(x^2/x^2-4/x^2) as x--> ~ y=lim(1+1/x^2)/(1-4/x^2) as x--> ~ y=1/1 y=1 is a horizontal asymptote |
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