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For f(x) = (2x + 5) / |3x - 4|, use graphs and tables to find the limit as x approaches infinity of f(x) and the limit as x approaches negative infinity of f(x)... Also identify any horizontal asymptotes...
Re: Infinite Limits
Horizontal asymptotes are the limits as x approaches infinity.
You're answers are correct. Whenever you have a polynomial division, where a*x^n and b*x^n are the highest terms for each the numerator and the denominator, than a horizontal asymptote exists at a/b. Note that both n's have to be the same. In other words, this does not apply to 5x^3 / 2x^2.
Edited to add:
if you have a*x^n and b*x^m as the highest terms in the polynomial division, then:
if n > m, the function goes to infinity
if n < m, the function has a horizontal asymptote at x = 0
if n = m, the function has a horizontal asymptote at a/b
Last edited by Ricky (2006-01-03 10:22:36)
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