Elements of the Differential and Integral Calculus with Examples and ApplicationsGinn, 1886 - 236 σελίδες |
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
1+x² a²y ABDP altitude angle Assume asymptote Ax=0 Ax ax² axis bx² constant cosec cycloid d²u d²y d³u d³y decreasing function differential distance dx dx dx dy dx dx Va² dx² dx³ dy² ellipse equal evidently Examine EXAMPLES exponent Find the area Find the equation finite fraction generatrix given Hence hyperbola increases increment indeterminate form infinite branch infinitesimals integral limit loga Maclaurin's formula maxima and minima maximum minimum multiple point Naperian logarithm negative obtain parabola plane curve point of inflexion polar POLAR CURVES positive prove radius rate of change ratio represent revolution sin x sin³ sinx slope subnormal Substituting these values subtangent tangent Taylor's formula total derivative variable velocity whole number x² dx Δα
Δημοφιλή αποσπάσματα
Σελίδα 78 - The weight of an object above the surface of the earth varies inversely as the square of its distance from the center of the earth.
Σελίδα 121 - A person being in a boat 3 miles from the nearest point of the beach, wishes to reach in the shortest time a place 5 miles from that point along the shore : supposing he can walk 5 miles an hour, but row only at the rate of 4 miles an hour, required the place where he must land.
Σελίδα 121 - A Norman window consists of a rectangle surmounted by a semicircle. Given the perimeter, required the height and breadth of the window when the quantity of light admitted is a maximum. The radius of the semicircle must equal the height of the rectangle.
Σελίδα 4 - The product of a constant and a variable 's also a variable, and the limit of the product of a constant and a variable is the product of the constant and the limit of the variable.
Σελίδα 14 - ... changed into the differential of the denominator, divided by the square of the denominator.
Σελίδα 13 - But, as dx • dy is the product of two infinitesimals, it is infinitely less than the other terms (ydx and xdy), and hence, having no value as compared with them, is to be dropped.* Therefore du = ydx + xdy.
Σελίδα 124 - ... component that is perpendicular to the keel of the ship, which is the only part of the original force that is effective in turning the ship, the expression to be made a maximum is sin
Σελίδα 171 - ... is called the circle of curvature of the curve (at that point). Its radius is the numerical value of the radius of curvature, and its center is the center of curvature.
Σελίδα 121 - ... shore ; he can pull at the rate of 4 miles an hour, but can walk at the rate of 5 miles an hour ; find the point at which he must land. Express the whole time in terms of the distance of the required point from the nearest point of the shore.
Σελίδα 95 - Taylor's Formula is a formula for developing a function of the sum of two variables in terms of the ascending powers of one of the variables, and finite coefficients which depend upon the other variable, the form of the function, and its constants.