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A Primer of Calculus

A Primer of Calculus


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About the Book

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. 1901 Excerpt: ...the straight line PS, since PS' does so; i.e., ds=lim NAs = lim arc PS'=PS. Observe that the two triangular figures PQP', PR'S', each with an arc side, are similar figures, with P as center of symmetry, and N as ratio of similitude. Since PR'S' approaches coincidence with the triangle PRS, it O M B L L' X appears that the difference figure PQP approaches similarity with the differential triangle PRS, as its sides indefinitely diminish. The difference figure reduces to the point P; we have left, however, in the triangle PRS what might be called its ultimate form. (a) The limiting ratio of any arc to its chord as the arc is taken smaller and smaller, is unity. For, PP' arc PP'=PS' arcPS', whose limit is PS: PS=l (b) The slope of the curve y=fx at the point (x, y) is dy /dx=f'x. For, the slope is tan f=RS/PR=dy/dx. (c) Inverse Principle 1. If dw--o identically, then w=constant. Or, if du=dv identically, then d(u--v)=o identically, and u--v=constant.' For the slope of y=fx being dy/dx, then if dy--o for a particular value of x, at such point (x, y) S coincides with R, or the tangent is parallel to OX; if dy=o for every value of x, then the tangent is parallel to OX at every point, and the curve y=fx must be a straight line parallel to OX, so that y=fx remains constant as x changes. This proves the principle for real functions of one real variable. More generally; f w be a real function of real independent variables x, y, then dw, = dx--dy, can be identically zero only when =o, =o, identically, since dx, dy, are arbitrary values. Thus v)=f(x, y) is constant when either x or y changes alone, whatever value the other variable may have, and it must then be constant when both vary, since Lf(x, y) = Ax/(x, y) + Ay/O', y)=o +o =o. Similarly for real functions of an...


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Product Details
  • ISBN-13: 9781130693089
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 24
  • Spine Width: 1 mm
  • Width: 189 mm
  • ISBN-10: 1130693082
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 64 gr

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