An Elementary Text-book on the Differential and Integral Calculus |
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An Elementary Text-Book on the Differential and Integral Calculus (Classic ... William Holding Echols No preview available - 2017 |
Common terms and phrases
a₁ a²ƒ absolutely convergent algebraic angle assigned asymptote ax² axis chord circle circular sectors constant continuous function converges coordinates corresponding curve cuts cx² cylinder definite integral determinate difference-quotient differential equation dx dx dx dy dx² dy dx ellipse equal evaluated EXAMPLES Find the area finite formula function f(x geometrical given Hence infinite inflexion intersection interval length limit maximum negative neighborhood normal ordinate origin P₁ parabola parallel perpendicular point of contact polynomial positive quadratic quotient radius of curvature rational function rectangle represented respect revolution revolving roots Show sin² singular point singular solution solution Solve straight line substitution surface symbol tangent plane theorem tion total derivative Trace volume x₁ x²/a² y₁ y²/b² дх ду
Popular passages
Page 391 - The order of a differential equation is the order of the highest derivative which occurs.
Page 155 - Cycloid is traced by a point on the circumference of a circle which rolls without slipping along a straight line.
Page 312 - A point moves so that the sum of the squares of its distances from the sides of an equilateral triangle is constant.
Page 465 - So 4- 104 pp. $1.10. The Tables, which are to five places of decimals, are regularly supplied to the United States Military Academy and to Princeton University and Yale University for the entrance examinations.
Page 305 - Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed points.
Page 397 - Find the curve in which the perpendicular from the origin upon the tangent is equal to the abscissa of the point of contact.
Page 229 - To find the locus of the foot of the perpendicular drawn from the origin to a tangent plane to any surface.
Page 395 - Determine the curve in which the polar subtangent is proportional to the length of the radius vector.
Page 169 - The limit of the sum of a finite number of functions is equal to the sum of their limits.
Page 344 - ... partly on one side, and partly on the other side of the principal railway, and that without reference to the title under which...