Analytic Geometry and Calculus by David Woods - Bookswagon
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Analytic Geometry and Calculus

Analytic Geometry and Calculus


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About the Book

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. 1917 edition. Excerpt: ...formulas Only one of the possible values has been given for each integral, as that single value is sufficient for all work. Referring to 1, 97, we see that sin-1-must be taken in the a first or the fourth quadrant; if, however, it is necessary to 3 x ] 5 To avoid fractions and radicals, we place dx Sdx _ 4 dx Ex.5. Find the value of f (j3+ x)'/x. J 5 + 4 x4 Separating the integrand into two fractions, that is, There is here a certain ambiguity, since tan_1V3 and tan_1(--1) have each an infinite number of values. If, however, we remember that the graph of tan_1x is composed of an infinite number of distinct parts, or branches, the ambiguity is removed by taking the values of tan-1 V;i and tan-1(--1) from = tan_1i--a 1 + a:2 tan-1 a and select any value of tan-1 a, then if b = a, tan-1/; must be taken equal to tan-1 a, since the value of the integral is then zero. As b varies from equality with a to its final value, tan_1i will vary from tan-1 a to the nearest value of tan-1'). The simplest way to choose the proper values of tan-1 J and tan_Iu is to take them both between----and-Then we have 114. Closely resembling formulas (1) and (2) of the last article in the form of the integrand are the following formulas: du f f = log(w +vm2+ a2)--log a. But log a is a constant and may accordingly be omitted from the formula of integration. If retained, it would affect the constant of integration only. To derive (2) we place u = a sec and proceed as in the derivation of (1). Formula (3) is derived by means of the fact that the fraction---may be separated into two fractions, the denominators u--a of which are respectively u--a and u + a; that is, 1 1/1 1 a + u ov J m + a and log(--1) is a constant complex quantity which can be ex pressed...


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Product Details
  • ISBN-13: 9781151882912
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 96
  • Spine Width: 5 mm
  • Width: 189 mm
  • ISBN-10: 1151882917
  • Publisher Date: 01 Apr 2013
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 186 gr


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