First Steps in the Calculus
First Steps in the Calculus
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In our eReader you can find the full English version of the book. Read First Steps in the Calculus 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 First Steps in the Calculus
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'. A2 lies between 7jPN 2 . Aas and 7rP'N' 2 . Asc, 261] INTEGRATION 417 A „ /. — lies between ttPN 2 and 7rP'N' 2 .
Ax Now. AsAa^O, g^g.
A „ But —, lying between 7rPN 2 and 7rP'N' 2, tends to equality with 7rPN 2 as Ax -*- 0.
... _ =lPN > = ^ =T, To find c, note that when x = 0, z = 0, . '. C = 0, 7rar* When a? = &, we have the volume of the cone the centre of base is B j viz.
7TO" 12' This is q-""(o) • 6= q 7rBS 2 . OB; in other words, * of the cylinder of the same base and height.
The result... -y- (volume) = ny* applies to the volume generated by the rotation of a curve about the axis of x; whatever function y is of x.
EXERCISE XXVI. E.
1. Y 2 = 4ax represents a parabola whose axis of symmetry is the sc-axis. By rotating the curve about the ir-axis, a paraboloid of revolution is formed. Of what form are sections of this surface made by planes perpendicular to the a?-axis? Of what form are sections made by planes containing the oj-axis ? Find the volume bounded by the paraboloid and a plane perpendicular to the aj-axis at x = b.
What to read after First Steps in the Calculus?
You can find similar books in the "Read Also" column, or choose other free books by C Charles Godfrey to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
'. A2 lies between 7jPN 2 . Aas and 7rP'N' 2 . Asc, 261] INTEGRATION 417 A „ /. — lies between ttPN 2 and 7rP'N' 2 .
Ax Now. AsAa^O, g^g.
A „ But —, lying between 7rPN 2 and 7rP'N' 2, tends to equality with 7rPN 2 as Ax -*- 0.
... _ =lPN > = ^ =T, To find c, note that when x = 0, z = 0, . '. C = 0, 7rar* When a? = &, we have the volume of the cone the centre of base is B j viz.
7TO" 12' This is q-""(o) • 6= q 7rBS 2 . OB; in other words, * of the cylinder of the same base and height.
The result... -y- (volume) = ny* applies to the volume generated by the rotation of a curve about the axis of x; whatever function y is of x.
EXERCISE XXVI. E.
1. Y 2 = 4ax represents a parabola whose axis of symmetry is the sc-axis. By rotating the curve about the ir-axis, a paraboloid of revolution is formed. Of what form are sections of this surface made by planes perpendicular to the a?-axis? Of what form are sections made by planes containing the oj-axis ? Find the volume bounded by the paraboloid and a plane perpendicular to the aj-axis at x = b.
What to read after First Steps in the Calculus?
You can find similar books in the "Read Also" column, or choose other free books by C Charles Godfrey to read onlineMoreLess
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