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 ( 52. ) и = ; find the maximum and minimum values ( 53. ) Show that the greatest ...
... 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 ( 52. ) и = ; find the maximum and minimum values ( 53. ) Show that the greatest ...
Halaman 94
... equation to the asymptote , and that the maximum ordinate is at the point indicated by x = 2 . ( 47. ) If C be the ... POLAR CO - ORDINATES . SPIRALS . 94 TANGENTS , NORMALS , ETC.
... equation to the asymptote , and that the maximum ordinate is at the point indicated by x = 2 . ( 47. ) If C be the ... POLAR CO - ORDINATES . SPIRALS . 94 TANGENTS , NORMALS , ETC.
Halaman 95
... polar equation to the common parabola . SP = r , ZASP = 0 . r = DN = 2AS + SN = 2a + rcos PSN = 2a - rcos0 . ∴r + rcos0 = 2a , 2a a r = 1 + cos 0 0 cos2 2 ( 2. ) The equation to the spiral of Archimedes is r = a0 ; find the angle ...
... polar equation to the common parabola . SP = r , ZASP = 0 . r = DN = 2AS + SN = 2a + rcos PSN = 2a - rcos0 . ∴r + rcos0 = 2a , 2a a r = 1 + cos 0 0 cos2 2 ( 2. ) The equation to the spiral of Archimedes is r = a0 ; find the angle ...
Halaman 96
... equation between p and r . 1 a + a cose a2 sin20 1 - = a + a cos 0 . .. u = и ( du ) 2 2 = 1 U But a cose : du = a ... POLAR CO - ORDINATES .
... equation between p and r . 1 a + a cose a2 sin20 1 - = a + a cos 0 . .. u = и ( du ) 2 2 = 1 U But a cose : du = a ... 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
2nd edition a²-x² a²+b² a²+x² angle asymptote asymptotic circle axes centre CHAPTER Charles Tomlinson chord co-ordinates common parabola considering constant contrary flexure cosec cosx cuts the axis d'u d'u d2y dx2 d³u diameter differential coefficient distance draw dx d2u dx dx dx dx dy dx² dx2 dy2 dxdy dy dy eliminate ellipse equal evolute find the equation formulæ fraction frustrum function given Hence hyperbola Inscribe the greatest intersection latus rectum locus Maclaurin's Theorem maximum or minimum normal NP=y origin osculating circle perpendicular point of contrary polar equation positive prove putting radius of curvature rectangular right-angles secx semi-cubical parabola sinx spiral straight line Strength of materials substituting subtangent tangent Taylor's theorem trace the curve tractory Treatise triangle u a maximum variable vertex vols vulgar fractions
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