A Treatise on the Differential Calculus |
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Page xii
... 1ƒ ( x , y ) r hv Rr f ( 0 ) 1 d d 1 12 h + k 1.2.3 dx dy 1.2.3 ( d d h + k dx dy 9 from bottom Co 7 17 18 18 εdz + dy r2de dr = α negative positive a03 v = { a 0 = τα dr positive negative - aos v = τα v = τα r2 de a Article Page.
... 1ƒ ( x , y ) r hv Rr f ( 0 ) 1 d d 1 12 h + k 1.2.3 dx dy 1.2.3 ( d d h + k dx dy 9 from bottom Co 7 17 18 18 εdz + dy r2de dr = α negative positive a03 v = { a 0 = τα dr positive negative - aos v = τα v = τα r2 de a Article Page.
Page 3
... positive quantity less than any assignable magnitude , it is plain that y also keeps continuously changing through every gradation of value from - 1 to ∞ but when --- x changes from a -h to a + h , y leaps from - ∞ to + ∞ without ...
... positive quantity less than any assignable magnitude , it is plain that y also keeps continuously changing through every gradation of value from - 1 to ∞ but when --- x changes from a -h to a + h , y leaps from - ∞ to + ∞ without ...
Page 4
William Walton. a being a positive quantity , it is plain that y will be imaginary whenever x is of the form 2λ + 1 2μ , A and μ being integers . Now between any two values of x , however little they may differ from each other , we may ...
William Walton. a being a positive quantity , it is plain that y will be imaginary whenever x is of the form 2λ + 1 2μ , A and μ being integers . Now between any two values of x , however little they may differ from each other , we may ...
Page 5
... positive value down to zero , but , the moment x becomes negative , y becomes impossible . The two branches corresponding to the double sign , each of which terminates abruptly at the origin , join together at this point and thus form a ...
... positive value down to zero , but , the moment x becomes negative , y becomes impossible . The two branches corresponding to the double sign , each of which terminates abruptly at the origin , join together at this point and thus form a ...
Page 25
... quantity that x ' = xz . Our object is now to find the limiting value of the fraction zn 2 -- 1 when z approaches indefinitely near to unity . Now whatever be the value of n , positive , integral , PRINCIPLES OF DIFFERENTIATION . 25.
... quantity that x ' = xz . Our object is now to find the limiting value of the fraction zn 2 -- 1 when z approaches indefinitely near to unity . Now whatever be the value of n , positive , integral , PRINCIPLES OF DIFFERENTIATION . 25.
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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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