Examples and Solutions in the Differential CalculusJohn Weale, 1851 - 186 halaman |
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Halaman 54
... polar diameter of the earth be to the equato- rial diameter as 229 : 230 ; show that the greatest angle made by a ... equation u3 - a2x + x = 0 . ecos cosx ( 52. ) u = - ; find the maximum and minimum values of u . t ( 53. ) Show ...
... polar diameter of the earth be to the equato- rial diameter as 229 : 230 ; show that the greatest angle made by a ... equation u3 - a2x + x = 0 . ecos cosx ( 52. ) u = - ; find the maximum and minimum values of u . t ( 53. ) Show ...
Halaman 94
James Haddon. ( 45. ) Draw a tangent to the curve , whose equation is y = ax m - 1 m " and ... equation to the asymptote , and that the maximum ordinate is at the point ... POLAR CO - ORDINATES . SPIRALS . 94 TANGENTS , NORMALS , ETC.
James Haddon. ( 45. ) Draw a tangent to the curve , whose equation is y = ax m - 1 m " and ... equation to the asymptote , and that the maximum ordinate is at the point ... POLAR CO - ORDINATES . SPIRALS . 94 TANGENTS , NORMALS , ETC.
Halaman 95
... polar equation to the common parabola . SP = r , LASP = 0 . r = DN = 2AS + SN = 2a + r cos PSN = 2a - r cos 0 . 2 a a : .r + rcos 0 = 2a , .r = 1+ cos 0 Ꮎ CoS2 ( 2. ) The equation to the spiral of Archimedes is r = a0 ; find the angle ...
... polar equation to the common parabola . SP = r , LASP = 0 . r = DN = 2AS + SN = 2a + r cos PSN = 2a - r cos 0 . 2 a a : .r + rcos 0 = 2a , .r = 1+ cos 0 Ꮎ CoS2 ( 2. ) The equation to the spiral of Archimedes is r = a0 ; find the angle ...
Halaman 96
... equation to that curve . dy dx T A S Also y - y = ( x , —x ) is the equation to the tangent . Differentiating the assumed equation , ax dy b dx a √2 2axx2 11 . dy in the equation to and substituting the values of 96 POLAR CO - ORDINATES .
... equation to that curve . dy dx T A S Also y - y = ( x , —x ) is the equation to the tangent . Differentiating the assumed equation , ax dy b dx a √2 2axx2 11 . dy in the equation to and substituting the values of 96 POLAR CO - ORDINATES .
Halaman 98
... equation referred to polar co - ordi- nates is r = a ( 1 - e2 ) 1+ e cose 1 ( 7. ) The equation to a curve being y = ( xm + axm - 1 ) m ; determine the polar equation , and show that an asymptote cuts the axis of abscissæ at an angle ...
... equation referred to polar co - ordi- nates is r = a ( 1 - e2 ) 1+ e cose 1 ( 7. ) The equation to a curve being y = ( xm + axm - 1 ) m ; determine the polar equation , and show that an asymptote cuts the axis of abscissæ at an angle ...
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Istilah dan frasa umum
1+p² 1+x² 2nd edition a²-x² a²+x² angle asymptote asymptotic circle axes centre CHAPTER Charles Tomlinson chord co-ordinates common parabola constant contrary flexure coseco cosx cuts the axis d²u d2u d2u d³u diameter differential coefficient distance dx d2u dx dx dx dx dy dx² e²x² eliminate ellipse equal evolute find the equation fraction frustrum function given Hence Henry Law hyperbola Inscribe the greatest intersection latus rectum locus logarithmic maxima and minima maximum or minimum negative normal NP=y origin osculating circle perpendicular point of contrary polar equation positive prove radius of curvature right-angles secx sinx spiral straight line substituting subtangent tan0 tangent Taylor's theorem trace the curve tractory Treatise triangle u a maximum values variable vertex vols vulgar fractions Whence
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