Differential Calculus with Applications and Numerous Examples: An Elementary Treatise...Macmillan, 1886 - 439 páginas |
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Página 135
... дф Here = 3 ( x2 — ay ) Эх dy x2 - ay дф dx y2 - ax and = 3 ( y2 — ax ) ду 146. Order of Partial Differentiations Commutative . Suppose we have any relation y = p ( x , a ) , where a is a constant , and that by differentiation we obtain ...
... дф Here = 3 ( x2 — ay ) Эх dy x2 - ay дф dx y2 - ax and = 3 ( y2 — ax ) ду 146. Order of Partial Differentiations Commutative . Suppose we have any relation y = p ( x , a ) , where a is a constant , and that by differentiation we obtain ...
Página 136
... дф ( х , у ) = дх Ltsy = 0 Eyp ( x , y ) . - дх = = a Ep ( x , y ) -p ( x , y ) Ltɛy = 0ǝx д -Ltsy = 0 дх ə Eyb ( x , y ) —p ( x , ? 1 ) oy бу Sy 147. Another Proof . The symbols and may also be 136 PARTIAL DIFFERENTIATION .
... дф ( х , у ) = дх Ltsy = 0 Eyp ( x , y ) . - дх = = a Ep ( x , y ) -p ( x , y ) Ltɛy = 0ǝx д -Ltsy = 0 дх ə Eyb ( x , y ) —p ( x , ? 1 ) oy бу Sy 147. Another Proof . The symbols and may also be 136 PARTIAL DIFFERENTIATION .
Página 143
... дф , 22 ф + Əx 2 ! Əx2 Эф + h + 724 + hk + джду ... 21 Əy2 1224 + + 2 ! Əy2 ... + ... = p ( x , y ) + ( h L + k ° P ) + Эх by 2 φ h2 + 2hk + k2 + ... Эхду Əy2 Əx2 or , as it may be written symbolically , ә h 212 p ( x + h , y + k ) = p ...
... дф , 22 ф + Əx 2 ! Əx2 Эф + h + 724 + hk + джду ... 21 Əy2 1224 + + 2 ! Əy2 ... + ... = p ( x , y ) + ( h L + k ° P ) + Эх by 2 φ h2 + 2hk + k2 + ... Эхду Əy2 Əx2 or , as it may be written symbolically , ә h 212 p ( x + h , y + k ) = p ...
Página 310
... дф дф 22 & 724 q a = ay h = = джду 826 and b Əy2 69. A curve is such that any two corresponding points of its evolute and an involute are at a constant distance . Prove that the line joining the two points is also constant in direction ...
... дф дф 22 & 724 q a = ay h = = джду 826 and b Əy2 69. A curve is such that any two corresponding points of its evolute and an involute are at a constant distance . Prove that the line joining the two points is also constant in direction ...
Página 315
... дф , дф ав Эфав дадла da + of + of d дад да - 0 , ...... = 0 .. ( 3 ) ( 4 ) We thus have four equations and three quantities to ав eliminate , viz . , a , ß , The result of elimination is the da equation of the envelope . The parameters ...
... дф , дф ав Эфав дадла da + of + of d дад да - 0 , ...... = 0 .. ( 3 ) ( 4 ) We thus have four equations and three quantities to ав eliminate , viz . , a , ß , The result of elimination is the da equation of the envelope . The parameters ...
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Differential Calculus With Applications and Numerous Examples: An Elementary ... Joseph Edwards Sin vista previa disponible - 2006 |
Términos y frases comunes
ALGEBRA angle Assistant-Master asymptote axis Cambridge cardioide centre chord circle co-ordinates coincident points conic Crown 8vo cusp cuts the curve cycloid denote differential coefficient dx dx dx dy dy dx ELEMENTARY ellipse envelope EXAMPLES Extra fcap fcap Fellow of Trinity Find function Globe 8vo Hence hyperbola independent variable infinite intersection intrinsic equation inverse John's College late Fellow limit LL.D locus MACMILLAN'S EDUCATIONAL CATALOGUE Mathematics maxima and minima minimum value negative normal ordinate origin Owens College p(x+h parabola parallel pedal equation perpendicular point of contact point of inflexion polar positive pedal PRIMER Professor prove quantity radius of curvature revised School Show straight line tangent Taylor's Theorem Trace the curve Trinity College ultimately coincident vanish whence zero ди ди ду дх Эф
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