## The elements of the differential and integral calculus: based on Kurzgefasstes Lehrbuch der differential- und integralrechnung |

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### Common terms and phrases

abscissa accordingly Analytic Geometry angle applied approaches the limit approaches zero approximation assume axes axis of abscissae Boyle's Law Calculus circle coefficients constant convergent coordinates corresponding values cos2 curve deduced definite integral denominator denote determine Differential Calculus differentiation distance dx dx dx ellipse equal to zero example EXERCISES exponential function expression factors Find the equation formula fraction function geometric h approaches hence homogeneous function hyperbola independent variable indeterminate forms inverse John Bernoulli length limit zero logarithms mathematics maxima and minima maximum method minimum negative notation obtain pair of numbers parabola parallel passes perpendicular point of intersection positive pressure problem quadrant quantity rectangle represent respectively result right member secant line second derivative straight line substituting tangent Taylor's Theorem temperature theorem tion triangle unity velocity volume whence z-axis

### Popular passages

Page 133 - 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 55 - 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 305 - 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 126 - The transform of the sum of two functions is equal to the sum of the transforms.

Page 382 - In a horizontal plane the distance d between two points A and B is known. Given, that the intensity of light varies directly as the sine of the angle of incidence ; and, inversely, as the square of the distance, to find at what height h, perpendicularly above A, an incandescent point must be situated in order that the intensity of light from it at the point B may be at a maximum. , , dV'2 Ans. h = — • 23. An open bin, with square base and vertical sides, is to hold a given volume of wheat. What...

Page 383 - A perpendicular lamp post is to be erected at a given horizontal distance d from a statue. What must be the height of the lamp above the head of the statue in order that the top of the head may be most strongly illuminated? HINT. According to physics, the intensity of the illumination is inversely proportional to the square of the distance of the light from the illuminated point, and directly proportional to the sine of the angle at which the rays of light (; siu LSP strike the object.

Page 94 - III. The limit of a fraction is the limit of the numerator divided by the limit of the denominator. Let x and y approach simultaneously the limits I and m x I respectively.

Page 411 - This volume by Dr. Brown is one of the best books on the subject. It should be studied by all, in order that any discussion of it, whether in the pulpit or in private conversation, should be intelligent.

Page 81 - The circumference of a circle is the limit which the perimeters of regular inscribed and circumscribed polygons approach when the number of...