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Further Examples: Interval

You can use Max and Min to find the endpoints of intervals.

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You can take the union and intersection of two or more intervals.

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Using IntervalMemberQ, you can check if an interval is contained in another.

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You can also check if a point belongs to an interval.

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You can do interval arithmetic with many functions. For example, this command reflects the fact that the square of any real number between -2 and 5 lies between 0 and 25.

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Taking the reciprocal gives two distinct intervals.

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You can use intervals in many kinds of functions.

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Some functions automatically generate intervals.

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With ordinary machine-precision arithmetic, this gives an incorrect result.

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The interval generated here, however, correctly includes the point 0.

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Interval arithmetic is useful in obtaining or proving bounds. Here we define a function ff, which depends on a parameter .

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This shows that ff is monotonically nonincreasing in x for all non-negative values of the parameter.

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