The Elements of the Differential and Integral Calculus: Based on Kurzgefasstes Lehrbuch Der Differential- und Integralrechnung Von W. Nernst und A. Schönflies |
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Common terms and phrases
a₁ abscissa accordingly Analytic Geometry angle approaches the limit approaches zero axes axis of abscissæ B₁ Boyle's Law Calculus circle constant convergent coördinates cos² curve deduced definite integral denominator denote determine Differential Calculus differentiation distance dy dx ellipse epsilon example EXERCISES exponential function expression factors Find the equation formula fraction function geometric given h approaches h₁ hence homogeneous function hyperbola increases independent variable inverse John Bernoulli length limit zero logarithms mathematics method negative notation obtain P₁ pair of numbers parabola parallel passes perpendicular point of intersection positive pressure problem quadrant quantity r₁ respectively result right member secant line sin x sin² straight line substituting tangent temperature theorem tion triangle Va² velocity volume x-axis x₁ y₁ ди
Popular passages
Page 135 - The derivative of the quotient of two functions is equal to the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.
Page 57 - PF'/PH'= e, by the definition of the curve. Furthermore :J (b) \PF—PF'\=2a. In fact, the hyperbola is often defined as the locus of a point which moves so that the difference of its distances from two fixed points is constant.
Page 307 - The bisector of an exterior angle of a triangle divides the opposite side externally into segments which are proportional to the other two sides.
Page 128 - The transform of the sum of two functions is equal to the sum of the transforms.
Page 384 - Given, that the intensity of light varies directly as the sine of the angle of incidence ; and, inversely, as the square of the distance...
Page 385 - According to physics, the intensity of the illumination is inversely proportional to the square of the distance of the light...