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Elements of Analytic Geometry and of the Differential and Integral Calculus (Paperback) Loot Price: R381
Discovery Miles 3 810

# Elements of Analytic Geometry and of the Differential and Integral Calculus (Paperback)

## Elias Loomis

Loot Price R381 Discovery Miles 3 810

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1859 Excerpt: ...differential of ax'y'? Ans.. Ex. 4. What is the differential of ax'(x'+2b)? Ans. Ex. 5. What is the differential of (x'+a) (2x+b) 1 Ans. Ex. 6. What is the differential of (x'+a) (3x'+b)? Ans. Proposition X.--Theorem. (182.) The differential of the product of any number of functions of the same variable, is equal to the sum of the products obtained by multiplying the differential of each function by the product of the others. Let us designate three functions by u, v, and z, and suppose them to depend on the same variable x. Substitute y for vz, and we shall have uvz=uy, ind d(uvz)--d(uy). But, by the preceding Proposition, d(uy)=ydu+udy;. (1) and since y=vz, we have, by the same Proposition, dy=zdv+vdz. Substituting these values of y and dy in equation (1), it becomes duvz)=vzdu+uzdv+uvdz. (2) The same method is applicable to the product of four or more functions. (183.) Cor. If we divide both members of equation (2) by uvz, we shall have dhtvz) du dv dz----=--+--+--, uvz uvz which is an extension of Art. 181. Ex. 1. What is the differential of xy'z? Ans. y'zdx+2xyzdy+xy, dz. Ex. 2. What is the differential of x'y'z'l Ans. Ex. 3. What is the differential of axy'z 1 Ans. Ex. 4. What is the differential of x(x'+a) (x+2b) 1 Ans. Ex. 5. What is the differential of ax(x'+a) (x+3b)? Ans. Proposition XI.--Theorem. (184.) The differential of a fraction is equal to the denominator into the differential of the numerator, minus the numerator into the differential of the denominator, divided by the square of the denominator. Let us designate the fraction by-, and suppose;= 0) then u=vy. I Therefore, by Prop. IX., du--ydv+vdy; whence vdy=du--ydv. (2) Substituting in the second member of equation (2) the value of y from equation (1), we have udv vdy--au. Dividing by v, we...

### General

 Imprint: Rarebooksclub.com Country of origin: United States Release date: March 2012 First published: March 2012 Authors: Elias Loomis Dimensions: 246 x 189 x 3mm (L x W x T) Format: Paperback - Trade Pages: 60 ISBN-13: 978-1-130-64161-5 Categories: Books > Humanities > History Books > Humanities > History > General Books > History > General LSN: 1-130-64161-9 Barcode: 9781130641615

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