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A limit gives us language for describing how function values (y-values) behave as the domain values (x-values) approach some particular number (or ∞ or -∞). In other words, a limit tells us:
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A limit gives us language for describing how function values (y-values) behave as the domain values (x-values) approach some particular number (or ∞ or -∞). • In other words, a limit tells us: • what the y-values of a function are approaching as x approaches some value c (but not necessarily equal to c) or it tells us • the intended y-value of a function as x approaches c (we will see this when x approaches a hole).
The limit as x approaches a number whose function value is definite:
The limit as x approaches an asymptote:(limits that fail to exist)
: Parent signature and test corrections on loose-leaf!!! Another example of when a limit fails to exist:
SUMMARY OF THE RELATIONSHIP BETWEEN HORIZONTAL AND VERTICAL ASYMPTOTES AND LIMITS: HORIZONTAL ASYMPTOTE VERTICAL ASYMPTOTE
END-BEHAVIOR MODEL (EBM) FOR RATIONAL FUNCTIONS: HOW DO WE USE THIS END-BEHAVIOR MODEL (EBM): EXAMPLE OF (EBM):
WHEN HAVE WE USED THE “EBM” IN A SIMILAR FASHION? To find horizontal asymptotes. LET’S EXAMINE THE PREVIOUS EXAMPLE MORE CLOSELY: