A Treatise on the Differential Calculus |
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Page 27
... ascertain the limiting value of the function n loga 1 + ( 1 - n when the integer n becomes great without limit . By the binomial theorem we have the following expansion , consisting of n + 1 terms , for 22 n 1 1 + n = 1 + 1 • n n 1+ viz ...
... ascertain the limiting value of the function n loga 1 + ( 1 - n when the integer n becomes great without limit . By the binomial theorem we have the following expansion , consisting of n + 1 terms , for 22 n 1 1 + n = 1 + 1 • n n 1+ viz ...
Page 108
... ascertain whether a particular value a of x , which makes dy dx = 0 , corresponds to a maximum or a minimum value of y , without being driven to the necessity of obtaining the general expression for the value of dry dx Ex . 1. Suppose ...
... ascertain whether a particular value a of x , which makes dy dx = 0 , corresponds to a maximum or a minimum value of y , without being driven to the necessity of obtaining the general expression for the value of dry dx Ex . 1. Suppose ...
Page 118
... ascertain whether x = 0 , y = 0 , which make dz O and dy = 0 , when z = x2 + x3y2 + y * , render z a maximum or a minimum . We have dz = 4x3 + 2xy2 = 0 , dx 2x3y + 4y3 = 0 , dz dy d2z da H 12x2 + 2y2 = 0 , d2z dxdy d2z dy2 d3z dx3 d3z ...
... ascertain whether x = 0 , y = 0 , which make dz O and dy = 0 , when z = x2 + x3y2 + y * , render z a maximum or a minimum . We have dz = 4x3 + 2xy2 = 0 , dx 2x3y + 4y3 = 0 , dz dy d2z da H 12x2 + 2y2 = 0 , d2z dxdy d2z dy2 d3z dx3 d3z ...
Page 120
... ascertain that all the partial differential coefficients of u below the nth must be equal to zero . In addition to this , we should find it to be necessary that a certain equation of n dimensions in y , z , the differential coefficients ...
... ascertain that all the partial differential coefficients of u below the nth must be equal to zero . In addition to this , we should find it to be necessary that a certain equation of n dimensions in y , z , the differential coefficients ...
Page 122
... ascertain whether D3u dx2 becomes , by the substitution of these values , negative in the former and positive in the latter case , 122 MAXIMA AND MINIMA . Application of indeterminate multipliers to problems of maxima and minima.
... ascertain whether D3u dx2 becomes , by the substitution of these values , negative in the former and positive in the latter case , 122 MAXIMA AND MINIMA . Application of indeterminate multipliers to problems of maxima and minima.
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Common terms and phrases
algebraical arbitrary functions asymptote axis Cambridge change sign constant cosec curve d'u dy d²r d²u d²x d²z d2z d2z d³u d³x d³y d³z denote df df df dx DIFFERENTIAL CALCULUS differential equations du du dy du² dv₁ dx dx dx dy dx dx dz dx² dx³ dxdy dy dF dy dx dy dy dy dy dz dy₁ dy₂ dy³ dz dx dz dy dz dz eliminate expression f(y₁ find the Differential formula ƒ Y₁ Hence implicit function increment independent variables indeterminate limit maxima and minima maximum or minimum minimum value multiplying negative partial differential coefficients points of inflection positive quantity putting regard shews Suppose tangent Taylor's Theorem total differential Trinity College University of Cambridge whence y+dy Y₁ Y₂ zero бу бх
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