This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1848 Excerpt: ...is an infinite branch; and when y is imaginary, the curve has no existence, on a perpendicular to the axis of the abscissas determined by the value of x. By this means, also, we may determine as many points in the curve as we please; and a line traced through these in the natural manner that will obviously suggest ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1848 Excerpt: ...is an infinite branch; and when y is imaginary, the curve has no existence, on a perpendicular to the axis of the abscissas determined by the value of x. By this means, also, we may determine as many points in the curve as we please; and a line traced through these in the natural manner that will obviously suggest itself, will approximate to the true curve as nearly as we please, the degree of approximation Moigno, Cournot, and other writers, give the curve whose equation is y = tan-i at--', as affording an instance of a point of this kind at the origin of its coordinates. This, however, is wrong as an infinite number of branches pass through the origin, not giving any angular point, but intersecting each other, and thus producing a multiple point. 144 ANALYSIS AND depending mainly on, the smallness of the intervals between the points so found. In the second place, for obtaining greater accuracy, we may find-L, and by this means we dx.may determine (No. 143) the angles at which the curve cuts the axis, if it do cut it, and (No. 127) the maximum and minimum values of y, if there be such. In the third place, we may (No. 1 48) find the asymptotes, if there be any: and, fourthly, to ensure still more precision, we may determine (by No. 165, and by the preceding part of this Section) the singular points, properly so called, if there be such. 232. To exemplify these principles, let us consider the curve of which the equation is y = a?--So? + 4. By assigning to x the values in the first line of the following table, we shall obtain those of y standing below them in the second line: x...... 0, dt oo, 1, 2, 3, 4, &c. y...... 4, oo 0, 0, 40, 180, &c. Hence we see, that the curve meets the axis of x, when x has any of the values, 1, 2, --1...
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PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.
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PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK.