IN MATH: 1. n. A function's values for extreme values of its variable; the value a function, f(x) approaches when x is extremely large or when x is extremely small; the function value, f(x) or y, approximated by the value of another function defined by the curve which is approached but never "reached" by a graph.

IN ENGLISH: 1. as defined above.

EX. 1:
When x is extremely large, the values of f(x) are close to the values of y = 0,
so, f(x) is positive and approximately 0.

When x is extremely small, the values of f(x) are close to the values of y = 0,
so, f(x) negative and approximately 0.
EX. 2:
When x is extremely large, the values of f(x) are close to the values of y = 4,
so, f(x) is approximately 4.

When x is extremely small, the values of f(x) are close to the values of y = 4,
so, f(x) negative and approximately 4.
EX. 3:
When x is extremely large, the values of f(x) are close to the values of y = -x + 4,
which is increasing infinitely, so, f(x) is increasing to positive infinitely.

When x is extremely small, the values of f(x) are close to the values of y = -x + 4,
which is decreasing infinitely, so, f(x) is decreasing to negaive infinity.
EX. 4:
When x is extremely large, the values of f(x) are close to the values of y = - x² + 4,
which is increasing infinitely, so, f(x) is decreasing to negaive infinitely.

When x is extremely small, the values of f(x) are close to the values of y = - x² + 4,
which is decreasing infinitely, so, f(x) is decreasing to negaive infinity.

APPLICATION: See list 230.


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