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Elements of the Differential Calculus with Examples and Applications; A Text Book

Elements of the Differential Calculus with Examples and Applications; A Text Book


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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. 1891 Excerpt: ...be either a maximum or a minimum, f(a + h)-fa must have the same sign for small values of h whether h is positive or negative.. If this sign is minus, fa is a maximum value of/lc; if plus, a minimum value (vide Art. 39). If fa does not equal zero, we can take a value of h so small, that, for it and all smaller values, /"(a + Oh) shall be less than/'-. The sign of Y'a + f"(a + ffh) will then, as h approaches zero, ultimately become and remain the same as the sign of Ufa; but the sign of life changes with the sign of h, so that fat can be neither a maximum nor a minimum. 144. Suppose fa = 0, then f(" + h)-fa = l/"- + fJ/"'(a + "'0 as h approaches zero--f'"(a + Oh) o! f"a will, in the end, become and remain less than-----and the quantity in parenthesis will have the same sign as/"a. As ft2 is, A necessarily positive for all values of h f(a + h)-fa will then be negative for small positive and negative values of h, if f"a is negative, and will be a maximum; if fa is positive, fa will be a minimum. 145. It can be easily established by an extension of the reasoning of the last section, that, if the first derivative that does not vanish when x = a is of odd order, fa is neither a maximum nor a minimum; that, if it is of even order and negative, fa is a maximum; if of even order and positive, fa is a minimum. Examples. (1) A body moves with different uniform velocities in two different media separated by a plane, required the path of quickest passage from a given point in the first medium to a given point of the second. It is easily seen that the required path will lie in a plane passing through the two given points and perpendicular to the plane separating the two media. Let ACB represent any such pat...


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Product Details
  • ISBN-13: 9781236251008
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 38
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1236251008
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 86 gr

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