 | William Shaffer Hall - Calculus - 1897 - 282 pages
...which the last term is the only fractional term. So it is necessary to consider only rational fractions in which the degree of the numerator is less than the degree of the denominator. A rational fraction is integrated by decomposing it into a number of simpler partial fractions, which... | |
 | Fletcher Durell, Edward Rutledge Robbins - Algebra - 1897 - 482 pages
...fractions by the use of the properties of identities. It is evident that if in the original fraction the degree of the numerator is less than the degree of the denominator, the same must be true in each partial or component fraction. The problem before us is the inverse of... | |
 | James Harrington Boyd - Algebra - 1901 - 812 pages
...factors partly of the first and partly of the second degree, or all of the second degree, in x, and the degree of the numerator is less than the degree of the denominator, we can separate the given fraction by means of the theorem of undetermined coefficients into partial... | |
 | James Harrington Boyd - Algebra - 1901 - 818 pages
...factors partly of tbe first arid partly of the second degree, or all of the second degree, in .r, and the degree of the numerator is less than the degree of the denominator, we can separate the given fraction by means of the theorem of undetermined coefficients into partial... | |
 | Louis Parker Jocelyn - Algebra - 1902 - 460 pages
...case it is terminating, in the latter, non terminating. 240. A Proper Fraction in the literal notation is one in which the degree of the numerator is less than the degree of the denominator. ILLUSTRATIONS. 241. An Improper Fraction in the literal notation is a fraction in which the degree... | |
 | William Charles Brenke - Algebra - 1910 - 376 pages
...factors. For reasons which will presently appear, the methods to be explained apply only to fractions in which the degree of the numerator is less than the degree of the denominator. When this is not the case, divide numerator by denominator until a remainder of less degree than the... | |
 | Edouard Goursat - Calculus - 1916 - 280 pages
...function, has a sense, provided that the denominator does not vanish for any real value of x and that the degree of the numerator is less than the degree of the denominator by at least two units. With the origin as center let us describe a circle C with a radius R large enough... | |
 | Edouard Goursat - Calculus - 1916 - 282 pages
...function, has a sense, provided that the denominator does not vanish for any real value of x and that the degree of the numerator is less than the degree of the denominator by at least two units. With the origin as center let us describe a circle C with a radius R large enough... | |
 | Edouard Goursat - Calculus - 1916 - 280 pages
...function, has a sense, provided that the denominator does not vanish for any real value of x and that the degree of the numerator is less than the degree of the denominator by at least two units. With the origin as center let us describe a circle C with a radius R large enough... | |
 | William Charles Brenke - Algebra - 1917 - 212 pages
...factors. For reasons which will presently appear, the methods to be explained apply only to fractions in which the degree of the numerator is less than the degree of the denominator. When this is not the case, divide numerator by denominator until a remainder of less degree than the... | |
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Q(x) to obtain a quotient (polynomial of the form g. ) plus a rational function (remainder divided by the divisor) in which the degree of the numerator is less than the degree of the denominator. 
