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#1 2006-01-02 11:01:33

Jacobpm
Guest

Infinite Limits

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...

When i graph the function in my graphing calculator, it looks like y will never reach a specific value as x approaches pos or neg infinity.. i went to table and checked at x value or 20000000 and -200000000 and i get 2/3 and -2/3 respectively

is this correct?
limit as x approaches pos inf = 2/3
limit as x approaches neg inf = -2/3

I'm not sure about the horizontal asymptotes?
would they be y = 2/3 and y = -2/3? I think? or is it something in between that?

Thanks for the input.

#2 2006-01-02 11:20:38

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Infinite Limits

Horizontal asymptotes are the limits as x approaches infinity.

If

where c is a constant, then the horizontal asymptote is x = c.  Same applies for negative 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 (2006-01-02 11:22:36)


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2006-01-02 11:22:31

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Infinite Limits

If x->+oo the function f is:
f(x)=(2x+5)/(3x-4). We'll find the limit:

Last edited by krassi_holmz (2006-01-02 11:30:05)


IPBLE:  Increasing Performance By Lowering Expectations.

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#4 2006-01-02 11:33:02

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Infinite Limits

Analogic,
                         2
   lim     f(x) = - ---
x--> -oo             3


IPBLE:  Increasing Performance By Lowering Expectations.

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