Examples of the Processes of the Differential and Integral Calculus |
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Page iii
... Problems illustrative of Theorems given in Elementary Treatises on the subject , but I have also introduced demonstrations of propositions which , although important and interesting , do not usually find a place in works devoted to the ...
... Problems illustrative of Theorems given in Elementary Treatises on the subject , but I have also introduced demonstrations of propositions which , although important and interesting , do not usually find a place in works devoted to the ...
Page v
... problem which is of frequent occurrence , but which I have not seen solved analyti- cally in any work in which the suffix notation is em- ployed . So long , therefore , as the old notation adapts itself to all cases in which it is ...
... problem which is of frequent occurrence , but which I have not seen solved analyti- cally in any work in which the suffix notation is em- ployed . So long , therefore , as the old notation adapts itself to all cases in which it is ...
Page vi
... problems which are interesting either from the nature of the questions involved , or from their bearing on the history of the Calculus . From a fear of increasing the size of the volume too much , I have not done this to as great an ...
... problems which are interesting either from the nature of the questions involved , or from their bearing on the history of the Calculus . From a fear of increasing the size of the volume too much , I have not done this to as great an ...
Page x
... Problems Involving the Solution of Differential Equations 440 XI . Evaluation of Definite Integrals 464 XII . Comparison of Transcendents 506 DIFFERENTIAL CALCULUS . CHAPTER I. DIFFERENTIATION . Functions of One X CONTENTS .
... Problems Involving the Solution of Differential Equations 440 XI . Evaluation of Definite Integrals 464 XII . Comparison of Transcendents 506 DIFFERENTIAL CALCULUS . CHAPTER I. DIFFERENTIATION . Functions of One X CONTENTS .
Page 96
... problem . Ex . ( 1 ) du == 1 u = x − x2 . - - 2x = 0 , whence x = = 1 ; da du 2 , and x = makes u = 49 1 , a maximum . dx2 ( 2 ) = u = x1 — 8 x3 + 22x2 - 24x + 12 . du dx = 4x3- 24x2 + 44x 24 = or x36x2 + 11x60 . = The roots of this ...
... problem . Ex . ( 1 ) du == 1 u = x − x2 . - - 2x = 0 , whence x = = 1 ; da du 2 , and x = makes u = 49 1 , a maximum . dx2 ( 2 ) = u = x1 — 8 x3 + 22x2 - 24x + 12 . du dx = 4x3- 24x2 + 44x 24 = or x36x2 + 11x60 . = The roots of this ...
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Common terms and phrases
a² b2 a²x² angle arbitrary constant assume asymptote becomes branches C₁ Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy dx dx² dy dx dy dy dy dy dz dz dz eliminate ellipse equal Euler factor formula fraction function Geometry gives Hence hypocycloid infinite intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral Multiply negative origin parabola perpendicular radius SECT singular points singular solution spiral Substituting subtangent surface tangent plane theorem triangle University of Cambridge vanish whence x²)³