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Calculus/Horizontal and Vertical Asymptote

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Expert: - 11/17/2008


Question
all i am asked to do is find all Horizontal and Vertical Asymptotes but the square root in the numerator is throwing me off...I don't even know where to begin.

f(x) = ((sqrt 5x^6-5)/4x^3-11x)

Answer
Is this suppose to be f(x) = √(5x^6-5) / (4x^3-11x)?

To find the horizontal assymptotes, look at the function as it goes to +∞ and -∞.  To do this divide the top and bottom by x^3, giving  
√(5+...) / (4...), so that the limit in either direction is √5 / 4.
This means there is a horizonatl assymptote at y = √5 / 4.

To find the vertical assymptotes, we need to see where the function is undefined.  To find the vertical assymptote, find where the denominator is 0.  This is at x(4x²-11) = 0, or x = 0 and x = ±√11/4.

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