Elements of the Differential And Integral Calculus, With Examples And Practical Applications
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In our eReader you can find the full English version of the book. Read Elements of the Differential And Integral Calculus, With Examples And Practical Applications 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 Elements of the Differential And Integral Calculus, With Examples And Practical Applications
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. (E) II 12. \L 92 DIFFERENTIAL AND INTEGRAL CALCULUS.
CoE. II. Differentiating (E), we have or Q* (T cosa; = l ---+--- — + etc. . . . (F) Cor. III. For the quantities within the parentheses in (D), substituting their values from (E) and (F), we have sin [y -\- x) ^= sin y cos x + cos y s,va.x. . . . (G) Cor. IV. Differentiating (G), regarding x as constant and y as variable, we have cos (y -{- x) = cos y cos x — sin y sin a;. . . . (H) 125. To develop log (y -\- x).
f{y -{- x) = log {y -\- x);... making x = 0, and differentiating, we have /(2/)-log(y); riy) = y, r%) = -^; r'(y) = J.; f'iy) = - ^^ ^t«- Substituting in (A), we have log (2/ + a;) = log (2/)+^- ^, + ^3 -etc., . , (I) which is the logarithmic series.
Cor. I. The nih. and {n + i)th terms of (I) are, omitting the signs, -. , , „ , , and — -; hence. Art. 117, = — ^-^, ^ {n — l)y ^^ ny"* a„ n ~1 which = y when « = oo . Therefore formula (I) is true when X is numerically less than y.
Cor. II. In (I), by making ?/ = 1, we have log(l + ^)=:.-^+y-^ + etc., .
What to read after Elements of the Differential And Integral Calculus, With Examples And Practical Applications?
You can find similar books in the "Read Also" column, or choose other free books by J W James William Nicholson to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
. (E) II 12. \L 92 DIFFERENTIAL AND INTEGRAL CALCULUS.
CoE. II. Differentiating (E), we have or Q* (T cosa; = l ---+--- — + etc. . . . (F) Cor. III. For the quantities within the parentheses in (D), substituting their values from (E) and (F), we have sin [y -\- x) ^= sin y cos x + cos y s,va.x. . . . (G) Cor. IV. Differentiating (G), regarding x as constant and y as variable, we have cos (y -{- x) = cos y cos x — sin y sin a;. . . . (H) 125. To develop log (y -\- x).
f{y -{- x) = log {y -\- x);... making x = 0, and differentiating, we have /(2/)-log(y); riy) = y, r%) = -^; r'(y) = J.; f'iy) = - ^^ ^t«- Substituting in (A), we have log (2/ + a;) = log (2/)+^- ^, + ^3 -etc., . , (I) which is the logarithmic series.
Cor. I. The nih. and {n + i)th terms of (I) are, omitting the signs, -. , , „ , , and — -; hence. Art. 117, = — ^-^, ^ {n — l)y ^^ ny"* a„ n ~1 which = y when « = oo . Therefore formula (I) is true when X is numerically less than y.
Cor. II. In (I), by making ?/ = 1, we have log(l + ^)=:.-^+y-^ + etc., .
What to read after Elements of the Differential And Integral Calculus, With Examples And Practical Applications?
You can find similar books in the "Read Also" column, or choose other free books by J W James William Nicholson to read onlineMoreLess
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