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How do you use limits to find a horizontal asymptote?

Answer 1

William Abdalla

Please see below.

We find limit of the function #f(x)# as #x->oo# i.e. #y=lim_(x->oo)f(x)#. An example is shown below.

Let the function be #f(x)=(ax^3+bx^2+cx+d)/(px^3+qx^2+rx+s)#,

then #lim_(x->oo)(ax^3+bx^2+cx+d)/(px^3+qx^2+rx+s)#.

Now dividing numerator and denominator by #x^3#, we get

#lim_(x->oo)(a+b/x+c/x^2+d/x^3)/(p+q/x+r/x^2+s/x^3)#

= #a/p#

and hence horizontal asymptote is #y=a/p#

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Answer 2

Isaiah Allen

To use limits to find a horizontal asymptote, you need to evaluate the limit of a function as it approaches positive or negative infinity. If the limit is a finite number, then that number represents the horizontal asymptote. If the limit is positive or negative infinity, or if it does not exist, then there is no horizontal asymptote.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.