The Principles of Fluxions Designed for the Use of Students in the University
The Principles of Fluxions Designed for the Use of Students in the University
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In our eReader you can find the full English version of the book. Read The Principles of Fluxions Designed for the Use of Students in the University 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 Principles of Fluxions Designed for the Use of Students in the University
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- 1 X = — . + hyp. Log. J 2x- X*, ^ 2X-X* J2X-X^ ^V ^ SI FLUENTS. 275 (344. ) Fluent 120.
To find the fluent of z'lfy, where % is the arc of a circle, and y the sine.
This fluent = ^^ - f. -^^ x z ; but ^ = /'^ _ I = y X 1 - "^ ' = (by the binomial theorem) ^ x : 1 + •2 — :Z + &c. And the whole fluent = -^ — — x : ~ 8r* w + 1 w+ 1 w + 2 + =L + r=^r + &C.
w + 4. 2r' 7z+6. 8r^ (345. ) Fluent 121.
To find the fluent of z^y, where z = the arc of a circle, and y the corresponding sine.
Let T = the r...adius, and x the cosine ; then, by Art. 44, ry = xzj and yz= —rx.
Assume v = z^i then, since the fluent of vy = vy-f. Yv, we have the fluent of z"y = zy -f. Y x nz'^'^z ; but yz=^rx; :, the second part =-^f. Nrz"-'x; and the fluent of this part = nz^'^rx -/. N. N-1, rxz'^'^z ; and since xz = ry, the fluent of the last term = - w . N- 1 . Z'^-^r'y + &c. Hence the required fluent = z^'y-^-n^'Wx-n . N— 1 . Z'^-^r^y - &c.
(346. ) The same fluent may be found in the following manner : Assume t/x : «z" + fez"~' + C2;'*~^+ &c.
What to read after The Principles of Fluxions Designed for the Use of Students in the University?
You can find similar books in the "Read Also" column, or choose other free books by William Dealtry to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
- 1 X = — . + hyp. Log. J 2x- X*, ^ 2X-X* J2X-X^ ^V ^ SI FLUENTS. 275 (344. ) Fluent 120.
To find the fluent of z'lfy, where % is the arc of a circle, and y the sine.
This fluent = ^^ - f. -^^ x z ; but ^ = /'^ _ I = y X 1 - "^ ' = (by the binomial theorem) ^ x : 1 + •2 — :Z + &c. And the whole fluent = -^ — — x : ~ 8r* w + 1 w+ 1 w + 2 + =L + r=^r + &C.
w + 4. 2r' 7z+6. 8r^ (345. ) Fluent 121.
To find the fluent of z^y, where z = the arc of a circle, and y the corresponding sine.
Let T = the r...adius, and x the cosine ; then, by Art. 44, ry = xzj and yz= —rx.
Assume v = z^i then, since the fluent of vy = vy-f. Yv, we have the fluent of z"y = zy -f. Y x nz'^'^z ; but yz=^rx; :, the second part =-^f. Nrz"-'x; and the fluent of this part = nz^'^rx -/. N. N-1, rxz'^'^z ; and since xz = ry, the fluent of the last term = - w . N- 1 . Z'^-^r'y + &c. Hence the required fluent = z^'y-^-n^'Wx-n . N— 1 . Z'^-^r^y - &c.
(346. ) The same fluent may be found in the following manner : Assume t/x : «z" + fez"~' + C2;'*~^+ &c.
What to read after The Principles of Fluxions Designed for the Use of Students in the University?
You can find similar books in the "Read Also" column, or choose other free books by William Dealtry to read onlineMoreLess
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