Asymptote of a FunctionDate: 06/02/2002 at 17:23:06 From: Sheryl Subject: Finding the value of a when horizontal asymptote is given I tried doing this question but I can't seem to figure it out. I really hope you can help me: Determine the value of a so that y = (ax + 5)/(3 - 6x) has a horizontal asymptote at y = -2/3 Date: 06/02/2002 at 20:53:03 From: Doctor Ian Subject: Re: Finding the value of a when horizontal asymptote is given Hi Sheryl, The thing about an asymptote is that when the value of x gets REALLY HUGE, the constant terms don't really contribute much to the value of the expression. For example, a(1,000,000,000) + 5 -------------------- 3 - 6(1,000,000,000) is just about the same as a(1,000,000,000) ----------------- -6(1,000,000,000) which is just about the same as a -- -6 Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 06/02/2002 at 22:22:23 From: Sheryl Subject: Finding the value of a when horizontal asymptote is given I still can't figure out how to find a. Date: 06/02/2002 at 22:29:08 From: Doctor Ian Subject: Re: Finding the value of a when horizontal asymptote is given Hi Sheryl, In the function ax + 5 f(x) = ------ 3 - 6x when x gets really large, it's nearly the same as ax a f(x) = --- = -- -6x -6 If the function is supposed to have an asymptote at f(x) = -2/3, the you need to find a value of a such that a -2 -- = -- -6 3 Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 06/02/2002 at 22:34:11 From: Sheryl Subject: finding the value of a when horizontal asymptote is given Yup! Thank you so much! |
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