An Introduction to the Calculus Based on Graphical Methods

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Macmillan, 1904 - 225 páginas
 

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Página 91 - If an arc of a plane curve revolve about an axis in its plane, not intersecting it, the surface generated is equal to the length of the arc multiplied by the length of the path of its mean centre.
Página 40 - Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm is -»- cm.
Página 56 - ... wall. 25. At what distance above the centre of a circle of radius a must an electric light be placed in order that the brightness at the circumference of the circle may be the greatest possible ? (Assume that the brightness of a small surface A varies inversely as the square of the distance r from a source of light, and directly as the cosine of the angle between r and the normal to the surface at A.) (Gibson's Calculus.) 78. Points of inflexion: rectangular coordinates. As a point moves along...
Página 40 - ... water varies as the cube of the speed, find the most economical rate of steaming against a current which is running at a given rate. 23. Assuming that the strength of a rectangular beam varies as the product of the breadth and the square of the depth of its cross-section...
Página 125 - Damping is calculated from the additional energy required to maintain constant amplitude. (1981) root-mean-square strain — the square root of the mean value of the square of the strain, averaged over one cycle of deformation.
Página 55 - N be the number of lines of force passing through a circuit, state in words the meaning of — dNjdt. 5. Express in symbols the statement that the electromotive force E is the sum of two terms of which the first is the product of the resistance R and the current C, and the second is the product of the selfinductance L and the time-rate of increase of C. 6. Express in symbols the statement that the force X acting on a magnetic shell in the direction x is equal to the space-rate of diminution in that...
Página 91 - Z-7rji/ds=ZTry xfds, ..................... (1) which is the theorem. 2°. If a plane area revolve about an axis in its plane, not intersecting it, the volume generated is equal to the area multiplied by the length of the path of its mean centre.
Página v - In the following pages an attempt has been made to present the psychology of number from this point of view.
Página 60 - From this point on, since 2.X" has the same meaning as ) Xi, 2X will be used to represent the summation of all the cases. 4-3 First Rule of Summation Rule 1. The summation of the sum of two or more terms is equal to the summation of the separate sums of the terms.
Página 178 - The curvature may be expressed in terms of the first and second derivatives of the ordinate at the point.

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