Elements of the Differential and Integral Calculus: With Examples and ApplicationsGinn, 1898 - 271 σελίδες |
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a²x a²x² area bounded assume asymptote au² ax² axis binomial theorem CHAPTER constant cos² cos³ curvature curve cusp cycloid d²y/dx² denote dx dx dx dy dz dx² dy dx dy/dx ellipse equal EXAMPLES Ə²u Find the area finite formulas fraction function Hence increment indefinite integral indeterminate form infinite infinitesimal limit locus logarithmic spiral maxima and minima maximum minimum of fx multiple point obtain ordinate parabola y² plane point of inflexion point of intersection polar curve positive radius rational revolution sec² sin x sin² sin³ sinm slope Substituting these values subtangent tangent Taylor's theorem theorem tractrix Va² variable velocity x-axis x2 dx x2dx xy² y-axis zero
Δημοφιλή αποσπάσματα
Σελίδα 235 - The order of a differential equation is the order of the highest derivative which occurs in it.
Σελίδα 224 - ... and measures the tendency of the force to produce rotation about the axis. The force exerted by gravity on a body varies as the mass of the body, and may be measured by the mass. The centre of mass 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 mass of any homogeneous body is the product of its volume by its density. 213. To find the centre of mass of a body. Let the points of the body be referred...
Σελίδα 88 - 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 90 - The captain of a man-of-war saw, one dark night, a privateersman crossing his path at right angles and at a distance ahead of c miles. The privateersman was making a miles an hour, while the man-of-war could make only b miles in the same time. The captain's only hope was to cross the track of the privateersman at as short a distance as possible under his stern, and to disable him by one or two well-directed shots ; so the ship's lights were put out and her course altered in accordance with this plan.
Σελίδα 253 - 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 229 - Ans. 4 п?аг. 216. The moment of inertia of a plane area about a given point in its plane is the limit of the sum. of the products obtained by multiplying the area of each infinitesimal portion by the square of its distance from the given point. Denote by MI the moment of inertia of the area NBCD, or A, about 0 (§ 207, fig.).
Σελίδα 12 - ... the limit of the product of a constant and a variable is the product of the constant by the limit of the variable.
Σελίδα 214 - Jo 2. Find the volume of a right conoid with circular base, the radius of the base being r, and the altitude a. Conceive the solid as generated by the section DTQ moving to the right, and denote OP its perpendicular distance from 0 by x.
Σελίδα 129 - Hence, if f(x, y) = 0 is below the wth degree in either x or y, there will be one or more asymptotes parallel to a co-ordinate axis. To find the equations of these asymptotes, equate to zero the coefficients of the highest powers of x and y.
Σελίδα 13 - But, as и is a general constant, mj' denotes any number ; hence (6), or [5], holds true for all values of и, т being a constant. The constant m is called the modulus of the system of logarithms whose base is a. The modulus of the common system of logarithms, obtained in § 97, is 0.434294 • • -. From the nature of logarithms we know that log„M changes the faster the smaller we take a.