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The concept of limits at infinity, focusing on end behavior and horizontal asymptotes. It includes examples, definitions, and guidelines for determining the behavior of functions as x approaches positive or negative infinity. The document also covers the BETC, BOBO, and BOTU rules for evaluating limits.
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Consider the "endbehavior" of a function on an (^) infinite interval.
Means that the limit exists and
In the example above, the value of y approaches 3 as x increases without bound. Similarly, f ( x ) approaches 3 as x decreases without bound.
The height that a function tries to, but cannot, reach as the function's x values get infinitely large or small. EX.#1: A function can have more than one horizontal asymptote.
Let's say we are trying to evaluate some function called r ( x ), which is defined as a fraction whose
A picture for your head. The guidelines below (^) only apply to limits at infinity so (^) be careful.
EX #3: Evaluate the following limits:
Final Note: Be sure you see that the equal sign in the statement does not mean that the limit exists. On the contrary, it tells you how the limit fails to exist by denoting the unbounded behavior of f ( x ) as x approaches c.
