as the denominator gets larger, the value of the fraction gets smaller. there is a horizontal...
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As the denominator gets larger, the value of the fraction gets smaller.
There is a horizontal asymptote if:
or
Example 2:Find:
When we graph this function, the limit appears to be zero.
so for :
by the sandwich theorem:
Infinite Limits:
As the denominator approaches zero, the value of the fraction gets very large.
If the denominator is positive then the fraction is positive.
If the denominator is negative then the fraction is negative.
vertical asymptote at x=0.
End Behavior Models:
End behavior models model the behavior of a function as x approaches infinity or negative infinity.
A function g is:
a right end behavior model for f if and only if
a left end behavior model for f if and only if
Test ofmodel
Our modelis correct.
Example 7:
As , approaches zero. (The x term dominates.)
becomes a right-end behavior model.
becomes a left-end behavior model.
As , increases faster than x decreases,therefore is dominant.
Test ofmodel
Our modelis correct.
Example 7:
becomes a right-end behavior model.
becomes a left-end behavior model.
On your calculator, graph:
Use: