This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1898 edition. Excerpt: ...units per second; and, as before, the actual rate of change at the instant denoted by t is lim AO=dO At = At dt' This is the number of current-units that would be gained in the next second if the rate of gain were uniform from the time t to the time t + 1. Since S. = Art. 21 dx dt dt hence measures the ...
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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1898 edition. Excerpt: ...units per second; and, as before, the actual rate of change at the instant denoted by t is lim AO=dO At = At dt' This is the number of current-units that would be gained in the next second if the rate of gain were uniform from the time t to the time t + 1. Since S. = Art. 21 dx dt dt hence measures the ratio of the rates of change of y dec and of x. It follows that the result of differentiating y=f(?) (i) may be written in either of the forms g =/'(), (2)!=/'()f. (3) The latter form is often convenient, and may also be obtained directly from (1) by differentiating both sides with regard to t. It may be read: the rate of change of y is f'(x) times the rate of change of x. Returning to the illustration of a moving point P, let its coordinates at time t be x and y; then measures the rate "dt of change of the-coordinate, and may be called the velocity of Jp resolved parallel to the z-axis, or the-component of the velocity. Similarly, & is the-compo Fig 24. nent of velocity. These three rates of change are connected by the equation Ex. 1. If a point describe the straight line Sx + y = 5, and if x increase h units per second, find the rates of increase of y and of s. Ex. 2. A point describes the parabola y2 = 12 x, in such a way that when x--3, the abscissa is increasing at the rate of 2 feet per second: at what rate is y then increasing? Find also the rate of increase of s. Ex. 3. A person is walking towards the foot of a tower on a horizontal plane at the rate of 5 miles per hour; at what rate is he approaching the top, which is 60 feet high, when he is 80 feet from the bottom? Let x be the distance from foot of tower at time t, and y the distance from the top at the same time; then X + 602 = y dx dy dt "dt When x is 80...
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Add this copy of Elements of the Differential Calculus to cart. $29.71, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2019 by Hansebooks.
Add this copy of Elements of the Differential Calculus to cart. $35.00, very good condition, Sold by Munster & Company rated 4.0 out of 5 stars, ships from Corvallis, OR, UNITED STATES, published 1898 by American Book Company.
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Seller's Description:
Very Good. No Jacket. New York: American Book Company, 1898. xiv, 337 pp. 21 x 15 cm. Dark blue-green cloth covered boards with gilt titling to spine. Bumping, rubbing, and wear to spine ends and corners of boards. Some light soiling and discoloration to boards. Mild to moderate age toning and dust soiling to edges of text block. Library bookplate on front pastedown and library pocket on rear free endpaper. Shallow dampstain to head of text block. Small stain on first blank page and adjacent pages. Interior otherwise clean and unmarked. Binding sound. Hard Cover. Very Good/No Jacket. Ex-Library.
Add this copy of Elements of the Differential Calculus to cart. $53.00, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2019 by hansebooks.
