Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
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Результати 1-5 із 61
Сторінка 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 ...
Сторінка 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 ...
Сторінка 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 ...
Сторінка 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 Χ 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 Χ CONTENTS .
Сторінка 96
... problem . Ex . ( 1 ) du dx = u = x - x2 . 1-2x = 0 , whence x = 2 , and x = makes u , a maximum . = u = x1 — 8 x3 + 22x2 - 24x + 12 . d2 u = dx2 J ( 2 ) du = 4x3- 24x2 + 44x - 24 = 0 , dx or 03-6x2 + 11x - 6 = 0 . The roots of this ...
... problem . Ex . ( 1 ) du dx = u = x - x2 . 1-2x = 0 , whence x = 2 , and x = makes u , a maximum . = u = x1 — 8 x3 + 22x2 - 24x + 12 . d2 u = dx2 J ( 2 ) du = 4x3- 24x2 + 44x - 24 = 0 , dx or 03-6x2 + 11x - 6 = 0 . The roots of this ...
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a² b2 a²x² angle arbitrary constant asymptote becomes C₁ c²x² Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy 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 plane of reference radius SECT singular solution spiral Substituting subtangent surface tangent plane theorem triangle vanish whence x²)³