Examples and Solutions in the Differential CalculusJohn Weale, 1851 - 186 halaman |
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Halaman 21
... positive or negative , integral or fractional , rational or irrational . Let u = ( a + x ) " , whence if x = 0 , U1 = a " . du - = n ( a + x ) " ~ 1 , . " U1 = nan - 1 . dx d2u dx2 = n ( n − 1 ) ( a + x ) n − 2 " U2 = n ( n − 1 ) an ...
... positive or negative , integral or fractional , rational or irrational . Let u = ( a + x ) " , whence if x = 0 , U1 = a " . du - = n ( a + x ) " ~ 1 , . " U1 = nan - 1 . dx d2u dx2 = n ( n − 1 ) ( a + x ) n − 2 " U2 = n ( n − 1 ) an ...
Halaman 36
... positive factor in the value of u . If u = a maximum or minimum , then u ” is a maximum or minimum if n is positive ; but when u = a maximum u TM ” is a minimum , and when ua minimum u- " is a maximum . Hence , before differentiating ...
... positive factor in the value of u . If u = a maximum or minimum , then u ” is a maximum or minimum if n is positive ; but when u = a maximum u TM ” is a minimum , and when ua minimum u- " is a maximum . Hence , before differentiating ...
Halaman 40
... positive result , d2u dx2 = 2+ .x = 6n2 ..u is a minimum . Hence the sum of the squares will be the smallest possible when the factors are equal , each being the square root of the given number . ( 7. ) Into how many equal parts must a ...
... positive result , d2u dx2 = 2+ .x = 6n2 ..u is a minimum . Hence the sum of the squares will be the smallest possible when the factors are equal , each being the square root of the given number . ( 7. ) Into how many equal parts must a ...
Halaman 42
... = = ( x —b ) 3 ( x - 1 ) 3 63 = + / ' a positive result , the area is a minimum . Since AD = 2AN , : . DE = 2DP , .. the line must be so drawn as to be bisected by the given point P. ( 12. ) From two points A , B , 42 MÁXIMA AND MINIMA .
... = = ( x —b ) 3 ( x - 1 ) 3 63 = + / ' a positive result , the area is a minimum . Since AD = 2AN , : . DE = 2DP , .. the line must be so drawn as to be bisected by the given point P. ( 12. ) From two points A , B , 42 MÁXIMA AND MINIMA .
Halaman 48
... positive result , y3 . the surface is a minimum . ( 22. ) The latitude of a place and two circles parallel to the horizon being given ; to determine the declination of a heavenly body , whose apparent time of passage from one circle to ...
... positive result , y3 . the surface is a minimum . ( 22. ) The latitude of a place and two circles parallel to the horizon being given ; to determine the declination of a heavenly body , whose apparent time of passage from one circle to ...
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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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