AP Calculus AB : Asymptotic behavior in terms of limits involving infinity
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Example Questions
Example Question #22 : Functions, Graphs, And Limits
Assume that a population of bunnies grows at a rate of 
Note: No integration is required for this problem.
70
350
5
700
350
The equation given is a model of logistic growth. Note that one of the other common forms this equation might be given in is 
Looking at the form of the derivative above, note that if we start with 14 bunnies, we get a positive derivative. This means that the population is increasing. As our function is continuous, the population will keep growing until the derivative hits 0. When does this occur?
In the above form, it should be more clear that the derivative is only 0 at 
Example Question #23 : Functions, Graphs, And Limits
The function 
The function will produce only positive outputs.
At x=0 the function is undefined.
The limit of the function as x-values approach 0 tends to either positive or negative infinity.
None of the other answers.
The function is discontinuous at y=0.
None of the other answers.
Unlike vertical asymptotes, horizontal asymptotes of certain functions may be crossed. In these cases, and in the case of the given function, the horizontal asymptote may be crossed and even have defined values laying on it (e.g., f(0)=0 for the function provided).
What is meaningful about the horizontal asymptote in this example is that it suggests the behavior of the function at large magnitudes. The denominator will increase much faster than the numerator. That is to say that the 
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