The Integration of Functions of a Single Variable
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In our eReader you can find the full English version of the book. Read The Integration of Functions of a Single Variable Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Integration of Functions of a Single Variable
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(i) The preceding argument fails if n < 3, but we have already seen that all conies are unicursal. The case next in importance is that of a cubic with a double point. If the double point is not at infinity we can, by a change of origin, reduce the equation of the curve to the form (ax + by) (ex + dy) =px 3 + 3qx 2 y + 3rxy' 2 + sy 3 ; and, by considering the intersections of the curve with the line y = tx, we find (a + bt) (c + dt) _ t(a + bt) (c + dt) °° ~ p + 3qt + 3rf + sf V ~p + Sqt + 'Srt* + sf ' If the double point is at infinity, the equation of the curve is of the form (ax + fiy) 2 (yx + By) + tx + £y + = 0, the curve having a pair of parallel asymptotes ; and, by considering the intersection of the curve with the line ax + (3y = t, we find 8tr> + & + /3d _ yf + €t + ad X ~ (/3y-a8)f+el3-ai;' V ~ (/3y - + <0 - af (ii) The case next in complexity is that of a quartic with three double points.
(a) The lemuiscate (x l + ?/ 2 ) 2 = a 2 (x 2 - y*) has three double points, the origin and the circular points at infinity.
What to read after The Integration of Functions of a Single Variable?
You can find similar books in the "Read Also" column, or choose other free books by G H Godfrey Harold Hardy to read online
To quickly assess the difficulty of the text, read a short excerpt:
(i) The preceding argument fails if n < 3, but we have already seen that all conies are unicursal. The case next in importance is that of a cubic with a double point. If the double point is not at infinity we can, by a change of origin, reduce the equation of the curve to the form (ax + by) (ex + dy) =px 3 + 3qx 2 y + 3rxy' 2 + sy 3 ; and, by considering the intersections of the curve with the line y = tx, we find (a + bt) (c + dt) _ t(a + bt) (c + dt) °° ~ p + 3qt + 3rf + sf V ~p + Sqt + 'Srt* + sf ' If the double point is at infinity, the equation of the curve is of the form (ax + fiy) 2 (yx + By) + tx + £y + = 0, the curve having a pair of parallel asymptotes ; and, by considering the intersection of the curve with the line ax + (3y = t, we find 8tr> + & + /3d _ yf + €t + ad X ~ (/3y-a8)f+el3-ai;' V ~ (/3y -
What to read after The Integration of Functions of a Single Variable?
You can find similar books in the "Read Also" column, or choose other free books by G H Godfrey Harold Hardy to read online
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