A Treatise on Infinitesimal Calculus: Differential calculus. 1857University Press, 1857 - Calculus |
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Results 6-10 of 56
Page 238
... minimum ; - to + , .. a minimum ; .. no max . or minimum ; x = 2 , and gives ... maximum value ; by a similar method the changes of sign due to the other ... maximum value at x 。. --- In fig . 13 , the reverse is the case ; as x ...
... minimum ; - to + , .. a minimum ; .. no max . or minimum ; x = 2 , and gives ... maximum value ; by a similar method the changes of sign due to the other ... maximum value at x 。. --- In fig . 13 , the reverse is the case ; as x ...
Page 239
... minimum ; x = x = - -2 , but does not change sign , .. no max . or minimum ; 5 and changes sign from + to - , 7 hence , when x = 1 , : ... a maximum ; F ( x ) = 0 , a minimum value ; 5 124 93 and when x = - F ( x ) = a maximum . 7 77 Ex ...
... minimum ; x = x = - -2 , but does not change sign , .. no max . or minimum ; 5 and changes sign from + to - , 7 hence , when x = 1 , : ... a maximum ; F ( x ) = 0 , a minimum value ; 5 124 93 and when x = - F ( x ) = a maximum . 7 77 Ex ...
Page 240
... maximum ; 5 п x = - to + , ... a minimum ; -- Hence the maximum value of the function is √2 , and the minimum is √2 ; which values recur whenever a is increased by π . 149. ] The change of sign of r ' ( x ) may often be conveniently ...
... maximum ; 5 п x = - to + , ... a minimum ; -- Hence the maximum value of the function is √2 , and the minimum is √2 ; which values recur whenever a is increased by π . 149. ] The change of sign of r ' ( x ) may often be conveniently ...
Page 241
... maximum and minimum values are to be determined ; then , by ( 21 ) , Art . 116 , F ( x + h ) − F ( x ) = hr ′ ( x + 0h ) ; - and if h is infinitesimal , F ' ( x + 0h ) becomes r ' ( x ) . Suppose now that x , is a value of x , such ...
... maximum and minimum values are to be determined ; then , by ( 21 ) , Art . 116 , F ( x + h ) − F ( x ) = hr ′ ( x + 0h ) ; - and if h is infinitesimal , F ' ( x + 0h ) becomes r ' ( x ) . Suppose now that x , is a value of x , such ...
Page 242
... maximum ; and if F ( x ) is positive , F ( x ) is a minimum . = Again , if " ( x ) = 0 , and F " " ( xo ) does not vanish , and if h is infinitesimal , F ( Xo + h ) − F ( X ) = h3 1.2.3 F " " ( xo ) ; in which case , as h3 changes its ...
... maximum ; and if F ( x ) is positive , F ( x ) is a minimum . = Again , if " ( x ) = 0 , and F " " ( xo ) does not vanish , and if h is infinitesimal , F ( Xo + h ) − F ( X ) = h3 1.2.3 F " " ( xo ) ; in which case , as h3 changes its ...
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a₁ algebraical angles b₁ becomes Calculus change of sign changes sign circle coefficients constant cosec curve d2F d2F d²u d²x d²y d³u d³y derived function determine differential equation dr dr dr dy dx dx dx dy dx² dy dx dy dy dy dz dy² dz dx equal equicrescent explicit function expression F(xo F(xo+h factor finite quantity fraction func given Hence homogeneous function increases increments indeterminate form infinite infinitesimal Infinitesimal Calculus infinity involved logarithms loge Maclaurin's maxima and minima maximum or minimum minimum value negative partial derived-functions positive primitive equation radius replaced result right-hand member roots Similarly sin x singular value Sturm's Theorem substituting suppose symbols Theorem tion vanish variables variation versin whence zero