Examples and Solutions in the Differential CalculusJohn Weale, 1851 - 186 halaman |
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Halaman 20
... prove that h h2 h3 = 1 + 2 + 2 ( 12+ ( 1 ) + ( 2 ) + & c . } . 1 - x - h1 - x 3 CHAPTER V. MACLAURIN'S THEOREM . This theorem , which is used for the development of a function according to the ascending powers of the variable , may be ...
... prove that h h2 h3 = 1 + 2 + 2 ( 12+ ( 1 ) + ( 2 ) + & c . } . 1 - x - h1 - x 3 CHAPTER V. MACLAURIN'S THEOREM . This theorem , which is used for the development of a function according to the ascending powers of the variable , may be ...
Halaman 25
... } = n2 " -3 { n + 3n } , . Whence , by substitution in the theorem , U3 = n22-3 ( n + 3 ) . n + 3 ) ( 1 + c ) = 2 ^ { 1 ++ ( n + 1 ) 22 + n2 ( n + 3 ) 23 12.2 D 23 1.2.3 + & c . } x2 x3 24 ( 7. ) Prove that log ( MACLAURIN'S THEOREM . 25.
... } = n2 " -3 { n + 3n } , . Whence , by substitution in the theorem , U3 = n22-3 ( n + 3 ) . n + 3 ) ( 1 + c ) = 2 ^ { 1 ++ ( n + 1 ) 22 + n2 ( n + 3 ) 23 12.2 D 23 1.2.3 + & c . } x2 x3 24 ( 7. ) Prove that log ( MACLAURIN'S THEOREM . 25.
Halaman 26
James Haddon. x2 x3 24 ( 7. ) Prove that log ( 1 + x ) = x - 2 + 3-4 + & c . Let u = log ( 1 + x ) , whence if x = 0 , U = log ( 1 ) = 0 . du 1 dx 1 + x = 1 - x + x2 - x2 + x4- & c . by actual division . But ( Maclaurin's Theorem . Cor ...
James Haddon. x2 x3 24 ( 7. ) Prove that log ( 1 + x ) = x - 2 + 3-4 + & c . Let u = log ( 1 + x ) , whence if x = 0 , U = log ( 1 ) = 0 . du 1 dx 1 + x = 1 - x + x2 - x2 + x4- & c . by actual division . But ( Maclaurin's Theorem . Cor ...
Halaman 27
... Prove Euler's formulæ , exe - x - 1 sinx = 21 COSx = ( 12. ) Prove De Moivre's formula , exte - x1 2 cosmx + √ - 1 sinmx = ( cosx + √ -1 sinx ) m . 4 6 x + & c . 5 ( 13. ) Prove that ( tanx ) = x2 + x ( 14. ) If usin ̄1æ , show that u ...
... Prove Euler's formulæ , exe - x - 1 sinx = 21 COSx = ( 12. ) Prove De Moivre's formula , exte - x1 2 cosmx + √ - 1 sinmx = ( cosx + √ -1 sinx ) m . 4 6 x + & c . 5 ( 13. ) Prove that ( tanx ) = x2 + x ( 14. ) If usin ̄1æ , show that u ...
Halaman 28
... Prove , by Maclaurin's theorem , that 7 ( 1 + 2x + 3x2 ) - $ = 1 - x + 2x -- x4 + x5- & c . π ( 17. ) Show that cosx = 2 х 2.3 325 2.3.4.5 ( 18. ) Show that sin ( a + bx + cx2 ) = sina + bx cosa + 2c cosa - b2sina 2 ( 19. ) Prove that ...
... Prove , by Maclaurin's theorem , that 7 ( 1 + 2x + 3x2 ) - $ = 1 - x + 2x -- x4 + x5- & c . π ( 17. ) Show that cosx = 2 х 2.3 325 2.3.4.5 ( 18. ) Show that sin ( a + bx + cx2 ) = sina + bx cosa + 2c cosa - b2sina 2 ( 19. ) Prove that ...
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2nd edition a²-x² a²+x² AB=a AN=x angle asymptote asymptotic circle axes catenary centre CHAPTER Charles Tomlinson chord co-ordinates common parabola considering constant contrary flexure coseco cot cosx cuts the axis cycloid d²u d2y dx2 d³u diameter differential coefficient differentiate with respect distance draw dx dx dx dx dy dx² dxdy dy dx dy² eliminate ellipse equal evolute find the equation formulæ frustrum function given Hence Henry Law infinite number Inscribe the greatest latus rectum length locus logarithms Maclaurin's Theorem maximum or minimum maximum ordinate normal NP=y origin osculating circle perpendicular point of contrary polar equation positive prove radii radius of curvature right-angles secx semi-cubical parabola sin2x sinx spiral straight line substituting subtangent tangent Taylor's theorem trace the curve tractory Treatise triangle variable vertex vols vulgar fractions whole numbers x²+y²
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