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In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions : The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it is a ...
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1]
1,3-Butanediol is an organic compound with the formula CH 3 CH (OH)CH 2 CH 2 OH. With two alcohol functional groups, the molecule is classified as a diol. The compound is also chiral, but most studies do not distinguish the enantiomers. The compound is a colorless, bittersweet, water-soluble liquid. It is one of four common structural isomers ...
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The indeterminate form is particularly common in calculus, because it often arises in the evaluation of derivatives using their definition in terms of limit. As mentioned above, (see fig. 1) while. (see fig. 2) This is enough to show that is an indeterminate form. Other examples with this indeterminate form include.
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