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When comparing and collating (sorting) text strings, different forms and rich text variants of characters should not alter the text processing results. For example, software users may be confused when performing a find on a page for a capital Latin letter 'I' and their software application fails to find the visually similar Roman numeral 'Ⅰ'.
Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...
The substitutions of Euler can be generalized by allowing the use of imaginary numbers. For example, in the integral +, the substitution + = + can be used. Extensions to the complex numbers allows us to use every type of Euler substitution regardless of the coefficients on the quadratic.
(For example, for fractions written in horizontal format, adding spaces to a fraction like 123456/127 would cause it to be misread as 123 456 / 127 or 1 23456 / 127 .) Markup: Templates {} or {} may be used to produce this formatting.
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Integration by substitution can be derived from the fundamental theorem of calculus as follows. Let and be two functions satisfying the above hypothesis that is continuous on and ′ is integrable on the closed interval [,].
For example, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. [2] [3] Thus, in the expression 1 + 2 × 3, the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9.
The following list includes the continued fractions of some constants and is sorted by their representations. Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue. Rational numbers have two continued fractions; the version in this list is the shorter one.