The Elements of the Differential and Integral Calculus: With Numerous Examples |
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Common terms and phrases
abscissas acceleration algebraic function angle approaches zero area inclosed Ax=0 Ax ax² axis Ay Ax body CHAPTER circular sectors concave constant curvature cycloid Definition Denote derivative differential direction displacement distance Divide double integration dx dy dx x=x0 dy dx equation EXAMPLE EXERCISES feet Find the area Find the coördinates Find the length force formulas given increases without limit infinite infinitesimal initial line limit Ay mass moment of inertia motion negative ordinates corresponding P₁ P₂ parabola parallel particle perpendicular plane polar coördinates positive preceding article radius rectangles required area respectively revolution Rolle's Theorem sec² Simpson's Rule sin² single valued speed subtangent surface tangent line Taylor's Theorem Theorem unit valued and continuous variable velocity x-axis x=xo xy-plane y-axis Δα
Popular passages
Page 350 - If a body is considered to be composed of a number of parts, its moment of inertia about an axis is equal to the sum of the moments of inertia of the...
Page 320 - ... attracts m at the distance r from m: m' J = K~^ . 246. It will be shown later (Art. 253) that the attraction of a homogeneous sphere at any external point is the same as if the mass of the sphere were concentrated at its center. Hence if m...
Page 67 - Assuming that the work of driving a steamer through the water varies as the cube of her speed, show that her most economical rate per hour against a current running с miles per hour is 3c/'2 miles per hour.
Page 67 - The work of propelling a steamer through the water varies as the cube of her speed. Find the most economical speed against a current running 4 miles per hour. Ans. 6 mi. per hr.
Page 308 - The work done by a force acting on a body to displace it is the product of the component of the force in the direction of the displacement and the displacement itself.
Page 65 - ... 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...
Page 66 - Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius 10 cm is -*- cm.
Page 66 - The strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from a circular cylindrical log of radius r. 22. The stiffness of a rectangular beam is proportional to the product of its breadth and the cube of its depth. Find the stiffest beam that can be cut from a log of given diameter.
Page 66 - Find the length of the shortest ladder that will reach from the ground to the house when leaning over the wall.
Page 308 - On the CGS system the unit of work is the work done when a force of one dyne is exerted through a distance of one centimetre.