Elementary Mathematical Analysis; A Text Book for First Year College Students

Elementary Mathematical Analysis; A Text Book for First Year College Students

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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. 1914 edition. Excerpt: ...x and y may be written y = r (2) Thus, when the values of a variable x run over an arithmetical progression (of first term 0) while the corresponding values of a variable y run over a geometrical progression (of first term 1), the relation between the variables may be written in either of the forms (1) or (2) above. Equation (2) is called an exponential equation and y is said to be an exponential function of x, while in (1) x is said to be a logarithmic function of y. The student has frequently been called upon in mathematics to express relations between variables in two different or "inverse" forms, analogous to the two forms y--rx and x = log, y. For example, he has written either y = x2 or: x = /y and either y = x"/2 x = J/2/" The graph of a function is of course the same whether the equation be solved for x or solved for y. 130. The student is required to construct the curves described in the following exercises by the method of 129. The inch, or 2 cm., may be adopted as the unit of measure; the curves should be drawn on plain paper within the interval from x =-2 to x = + 2. If tangents be drawn to the curves at x =--2, --1, 0, 1, 2, it will be noted, as nearly as can be determined by experiment, that the several tangents to any one curve cut the X-axis at the same constant distance to the left of the ordinate of the point of tangency. This distance is greater than unity if r = 2 and less than unity if r = 3. The value of r for which the distance is exactly unity is later shown to be a certain irrational or incommensurable number, approximately 2.7183..., represented in mathematics by the letter e, and called the Naperian base. This number, and the number ir, are two of the most important and fundamental...show more

Product details

  • Paperback | 108 pages
  • 189 x 246 x 6mm | 209g
  • Rarebooksclub.com
  • Miami Fl, United States
  • English
  • black & white illustrations
  • 1236522788
  • 9781236522788