A treatise on the integral calculus and its applications1857 |
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Página 22
... unity . Suppose V = ( x − a ) ( x − b ) ” ( x2 − 2ax + a2 + B2 ) ( x2 − 2yx + y2 + 82 ) , so that the equation V = 0 has ( 1 ) one real root = a , ( 2 ) r equal real roots , each = b , ( 3 ) a pair of imaginary roots a ± ẞ √ ( − 1 ) ...
... unity . Suppose V = ( x − a ) ( x − b ) ” ( x2 − 2ax + a2 + B2 ) ( x2 − 2yx + y2 + 82 ) , so that the equation V = 0 has ( 1 ) one real root = a , ( 2 ) r equal real roots , each = b , ( 3 ) a pair of imaginary roots a ± ẞ √ ( − 1 ) ...
Página 44
... sin xdx , which is unity . Hence , if n be an integer , sin ” xda : = [ " sin " sin ” xdc = - ( n − 1 ) ( n − 3 ) ( n 5 ) ...... 1 T - n ( n − 2 ) ( n − 4 ) ...... 2 - - ( n − 1 ) ( n − 3 ) ( n − 5 ) ............ ..2 - - n ...
... sin xdx , which is unity . Hence , if n be an integer , sin ” xda : = [ " sin " sin ” xdc = - ( n − 1 ) ( n − 3 ) ( n 5 ) ...... 1 T - n ( n − 2 ) ( n − 4 ) ...... 2 - - ( n − 1 ) ( n − 3 ) ( n − 5 ) ............ ..2 - - n ...
Página 45
... right hand member of ( 2 ) is less than unity and greater than n - 1 n ; thus π > and < 2.2.4.4.6.6 ............... . ( n − 2 ) ( n − 2 ) 1.3.3.5.5.7 · ( n − 3 ) ( n − 1 ) ...... - - - " 2.2.4.4.6.6 ............... . ( n − 2 ) ( n − ...
... right hand member of ( 2 ) is less than unity and greater than n - 1 n ; thus π > and < 2.2.4.4.6.6 ............... . ( n − 2 ) ( n − 2 ) 1.3.3.5.5.7 · ( n − 3 ) ( n − 1 ) ...... - - - " 2.2.4.4.6.6 ............... . ( n − 2 ) ( n − ...
Página 53
... unity , and by taking a suffici- ently near to unity , we can make the value of the integral differ as little as we please from 2. " 46. Next take ୮ " a dx 1 Xx the value of this integral is — log ( 1 − a ) which increases ...
... unity , and by taking a suffici- ently near to unity , we can make the value of the integral differ as little as we please from 2. " 46. Next take ୮ " a dx 1 Xx the value of this integral is — log ( 1 − a ) which increases ...
Página 95
... unity . For example , if s = 1 sin 2 , 8 = 1 sing , s = 1 sin 2 , 3 h s = 1 sing , 22 .... 1 3 we have epicycloids in which - = " a 1 , 2 , ... If s = l sin 24 , s = l sin 34 , s = 7 sin 40 , s = 7 sin 54 , ... b we have hypocycloids in ...
... unity . For example , if s = 1 sin 2 , 8 = 1 sing , s = 1 sin 2 , 3 h s = 1 sing , 22 .... 1 3 we have epicycloids in which - = " a 1 , 2 , ... If s = l sin 24 , s = l sin 34 , s = 7 sin 40 , s = 7 sin 54 , ... b we have hypocycloids in ...
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A Treatise on the Integral Calculus and Its Applications with Numerous Examples Isaac Todhunter Visualização integral - 1878 |
A Treatise on the Integral Calculus and Its Applications with Numerous Examples Isaac Todhunter Visualização integral - 1886 |
Palavras e frases frequentes
Application c² sin² Cambridge circle cloth co-ordinates constant cos² cos³ Crown 8vo curve cycloid definite integral denote differential coefficient double integral dx dx dx dy dz dy dx dz dx element ellipse equal Eulerian integral example expression Fcap Fellow of St Find the area find the volume formula function Hence indefinitely Integral Calculus integrate with respect intrinsic equation John's College latus rectum length limits M.A. Fellow MACMILLAN & CO.'S numerous obtain ordinate parabola partial fractions perpendicular plane positive preceding article radius vector result revolution revolve round round the axis shew sin² solid suppose surface tangent tion tractory transformed integral Trinity College unity vanishes variables vertex x₁ Y₁ πα аф
Passagens conhecidas
Página 13 - Prize Essay for 1877. 8vo. 8.r. 6V. SMITH— Works by the Rev. BARNARD SMITH, MA, Rector of Glaston, Rutland, late Fellow and Senior Bursar of St. Peter's College, Cambridge. ARITHMETIC AND ALGEBRA, in their Principles and Application ; with numerous systematically arranged Examples taken from the Cambridge Examination Papers, with especial reference to the Ordinary Examination for the BA Degree.
Página 8 - Essays, Biographical and Critical; chiefly on the English PoetS. By DAVID MASSON, MA Professor of English Literature in University College, London.
Página 16 - THE SEVEN KINGS OF ROME. An Easy Narrative, abridged from the First Book of Livy by the omission of Difficult Passages; being a First Latin Reading Book, with Grammatical Notes and Vocabulary.
Página 4 - Law," in which a comparison is occasionally made between the Roman Laws and those of England, by Samuel Hallifax, late Lord Bishop of St.
Página 15 - The fitness of Holy Scripture for Unfolding the Spiritual Life of Man : Christ the Desire of all Nations ; or, the Unconscious Prophecies of Heathendom.
Página 2 - The Evidences of Christianity as Exhibited in the Writings of its Apologists down to Augustine. An Essay which obtained the Hulsean Prize for the Year 1852. By WJ BOLTON, of Gonville and Caius College, Cambridge. 8vo. cloth, 6s.
Página 2 - W. ARCHER BUTLER, late Professor of Moral Philosophy in the University of Dublin. Edited, from the Author's Manuscripts, by WILLIAM HEPWORTH THOMPSON, MA Regius Professor of Greek in the University of Cambridge.
Página 4 - FROST.— The First Three Sections of Newton's Principia. With Notes and Problems in illustration of the subject. By PERCIVAL FROST, MA late Fellow of St. John's College, Cambridge, and Mathematical Lecturer of Jesus College. Crown 8vo. cloth, 10s.
Página 12 - PUCKLE.— An Elementary Treatise on Conic Sections and Algebraic Geometry. With a numerous collection of Easy Examples progressively arranged, especially designed for the use of Schools and Beginners. By G. HALE PUCKLE, MA, Principal of Windermere College.