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In the top figure the fraction 1/9000 in Excel is displayed. Although this number has a decimal representation that is an infinite string of ones, Excel displays only the leading 15 figures. In the second line, the number one is added to the fraction, and again Excel displays only 15 figures.
Indeterminate form is a mathematical expression that can obtain any value depending on circumstances. In calculus , it is usually possible to compute the limit of the sum, difference, product, quotient or power of two functions by taking the corresponding combination of the separate limits of each respective function.
However, when a function is constructed by dividing two functions whose separate limits are both equal to , then the limit of the result cannot be determined from the separate limits, so is said to take an indeterminate form, informally written . (Another indeterminate form, , results from dividing two functions whose limits both tend to ...
Another meaning for generalized continued fraction is a generalization to higher dimensions. For example, there is a close relationship between the simple continued fraction in canonical form for the irrational real number α, and the way lattice points in two dimensions lie to either side of the line y = αx. Generalizing this idea, one might ...
When given a ratio between two functions, the limit of this ratio can be evaluated by computing the limit of each function separately. Where the limit of the function in the denominator is infinity, and the numerator does not allow the ratio to be well determined, the limit of the ratio is said to be of indeterminate form. [9] An example of ...
To begin solving, we multiply each side of the equation by the least common denominator of all the fractions contained in the equation. In this case, the least common denominator is () (+). After performing these operations, the fractions are eliminated, and the equation becomes:
To satisfy those wishing a more strict interpretation of how the power function should act, the 2008 standard defines two additional power functions: pown(x, n), where the exponent must be an integer, and powr(x, y), which returns a NaN whenever a parameter is a NaN or the exponentiation would give an indeterminate form.
In the second case, indeterminate generally indicates that a value or property can have many meaningful definitions. Additionally, it seems to be generally accepted that undefined values may not be safely used within a particular formal system, whereas indeterminate values might be, depending on the relevant rules of the particular formal ...