Elements of the Differential Calculus: With Examples and Applications |
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Common terms and phrases
Analytic Geometry angle approaches zero axis Binomial Theorem body called centre chord circle constant coördinates corresponding increments cosy cycloid D₁ D₂ D₂u D₂x D₂y D₂y)² D³y decreases definite value descent developed difference differential dx² dy dx earth ellipse equal zero equation evolute EXAMPLES expression finite formulas function fx Fx given curve given point hence higher order hn+1 increases indefinitely independent variable Indeterminate Forms infinitely near points integral length limit Ay limiting position locus loga Maxima and Minima maximum mean velocity minimum values multiplied negative normal obtained ordinate parabola perpendicular plane principal infinitesimal radii radius of curvature ratio rectangle secant line second order sin² sinx Suppose tangent Taylor's Theorem tesimal tion true value vertex xn+1 xo+h y=fx Δα Δυ
Popular passages
Page 167 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 164 - T'PR= T'PF, and the tangent at any point of a parabola bisects the angle between the focal radius and the diameter through the given point.
Page 252 - F™a=f< n ia, the curves are said to have contact of the nth order at the point whose abscissa is a. Contact of a higher order than the first is called osculation. 238. The difference between the ordinates of points of the two curves having the same abscissa and infinitely near the point of contact, is an infinitesimal of an order one higher than the order of contact of the curves. Let...
Page 167 - If two right-angled triangles have the hypothenuse and a side of the one equal to the hypothenuse and a side of the other, each to each, the triangles are equal. Let...
Page 190 - The Centre of Gravity of a body is a point so situated that the force of gravity produces no tendency in the body to rotate about any axis passing through this point. The subject of centres of gravity belongs to Mechanics, and...
Page 33 - Dxy, which is, by Art. 27, the tangent of the inclination of the curve to the axis, must equal zero. Of course it does not follow from the argument just presented, that every value of x that makes...
Page 39 - 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. Ans.