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Elements of the Differential Calculus: With Examples and Applications, Volum 25
William Elwood Byerly
Uten tilgangsbegrensning - 1888
_ limit abscissa actual velocity Algebraic Functions angle approaches zero Ax approaches axis Binomial Theorem called centre chord circle constant coordinates corresponding increments cosx curvature cycloid decreasing definite value difference differential distance fallen equation evolute Examples expression find the derivative finite formulas fraction Fx Fx geometry given curve given point hence increases indefinitely indefinitely increased independent variable Indeterminate Forms infinitely near points instant integral length limit approached limiting position Maxima and Minima maximum mean velocity method minimum values moving body negative normal number of sides obtained Osculating circle parabola particular value plane curve polygon principal infinitesimal problems quantity radius radius of curvature ratio rectangle secant line second point sinx subtangent Suppose t0 seconds tangent tanr Taylor's Theorem tive Trigonometric Functions true value value xo variable increases vertex whole number
Side 87 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Side 257 - Universities, and is intended for a text-book, and not for an exhaustive treatise. Its peculiarities are the rigorous use of the Doctrine of Limits, as a foundation of the subject, and as preliminary to the adoption of the more direct and practically convenient infinitesimal notation and nomenclature ; the early introduction of a few simple formulas and methods for integrating ; a rather elaborate treatment of the use of infinitesimals in pure geometry ; and the attempt to excite and keep up the...
Side xv - Ax representing a single quantity. It is to be noted that as an increment is a difference, it may be either positive or negative. 5. If a variable which changes its value according to some law can be made to approach some fixed, constant value as nearly as we please, but can never become equal to it, the constant is called the limit of the variable under the circumstances in question. 6. For example ; the limit of -, as n increases indefinitely, is...
Side 184 - 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...
Side 27 - 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...
Side 255 - ... Geometry for Beginners, but it is shorter and easier, and does not require a knowledge of the metric system. Like the Geometry for Beginners this is especially commended to those who cannot pursue the study far but desire the discipline of geometry. CC Bounds, Prin. State Normal School, Plymouth...