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A common solution is to initially compute the sine of many evenly distributed values, and then to find the sine of x we choose the sine of the value closest to x through array indexing operation. This will be close to the correct value because sine is a continuous function with a bounded rate of change. [10]: 6 For example: [11]: 545–548
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In multivariable calculus, an iterated limit is a limit of a sequence or a limit of a function in the form , = (,), (,) = ((,)),or other similar forms. An iterated limit is only defined for an expression whose value depends on at least two variables. To evaluate such a limit, one takes the limiting process as one of the two variables approaches some number, getting an expression whose value ...
Then, for example, some generalizations of the Banach fixed-point theorem are: Assume that some iterate T n of T is a contraction. Then T has a unique fixed point. Assume that for each n, there exist c n such that d(T n (x), T n (y)) ≤ c n d(x, y) for all x and y, and that <.
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
Unless each then-clause and else-clause is carefully tested, to watch for extra newlines, then the results are likely to cause broken lines, with extra line breaks for each newline. For that reason, a global edit with simple search-and-replace of " {#if: " to " {if|| " is likely to leave newline problems, wherever the original markup was ...
For such a double limit to exist, this definition requires the value of f approaches L along every possible path approaching (p, q), excluding the two lines x = p and y = q. As a result, the multiple limit is a weaker notion than the ordinary limit: if the ordinary limit exists and equals L, then the multiple limit exists and also equals L. The ...