The Elements of Plane And Solid Analytic Geometry
The Elements of Plane And Solid Analytic Geometry
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In our eReader you can find the full English version of the book. Read The Elements of Plane And Solid Analytic Geometry 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 Elements of Plane And Solid Analytic Geometry
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Therefore, since the graph of f(x) is a continuous curve ( 64), in passing from A to B along the graph the x-axis will be crossed an even number, or an odd number, of times according as /(a) and f(b) have the same sign, or opposite signs. This proves the proposition. (An even number includes the case of no roots. ) E. G. If /(x) = x* - 3x + 1, then /(I) = - 1 and/(2) = 3.
, -. At least one real root of x 3 3x + 1 =0 lies between 1 and 2.
71. ^Ln equation of an odd degree 7ias at least one real ...root. Let the given equation be Let a be a positive value of x sufficiently large to make the first term of /(a) greater than the sum of all the other terms ( 69). Then the sign of /(a) will be the same as the sign of a 2?l+1, i. E. The same as the sign of a.
Hence if a be sufficiently great, f(a) is positive, /(O) =p 2n +i> and /( a) is negative.
Therefore in all cases there is one real root, which is positive or negative according as p 2n+l is negative or positive ( 70).
78] THEORY OF EQUATIONS 89 Hence the graph of a function of an odd degree in the standard form extends to infinity in the first and third quadrants.
What to read after The Elements of Plane And Solid Analytic Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Albert L Albert Luther Candy to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Therefore, since the graph of f(x) is a continuous curve ( 64), in passing from A to B along the graph the x-axis will be crossed an even number, or an odd number, of times according as /(a) and f(b) have the same sign, or opposite signs. This proves the proposition. (An even number includes the case of no roots. ) E. G. If /(x) = x* - 3x + 1, then /(I) = - 1 and/(2) = 3.
, -. At least one real root of x 3 3x + 1 =0 lies between 1 and 2.
71. ^Ln equation of an odd degree 7ias at least one real ...root. Let the given equation be Let a be a positive value of x sufficiently large to make the first term of /(a) greater than the sum of all the other terms ( 69). Then the sign of /(a) will be the same as the sign of a 2?l+1, i. E. The same as the sign of a.
Hence if a be sufficiently great, f(a) is positive, /(O) =p 2n +i> and /( a) is negative.
Therefore in all cases there is one real root, which is positive or negative according as p 2n+l is negative or positive ( 70).
78] THEORY OF EQUATIONS 89 Hence the graph of a function of an odd degree in the standard form extends to infinity in the first and third quadrants.
What to read after The Elements of Plane And Solid Analytic Geometry?
You can find similar books in the "Read Also" column, or choose other free books by Albert L Albert Luther Candy to read onlineMoreLess
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