By David Machin (auth.)
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Additional info for Biomathematics: An Introduction
This is only true if lxl < 1 (that is, the absolute value of x is less than one: by absolute value or modulus we mean the value ignoring the sign). It is also clear that for . to ( 1 + x )10 by x = 1/1 00 we h a d a very accurate approxLmatLon 49 taking the first few terms of the binomial expansion. 12) means 'approximately equal to'. 10 to a reasonable degree of accuracy. 12 in chapter 4. We should also note, again provided x is small, that the approximation may be used for non-integer and negative indices.
6 is then known as a polynomial of degree n. The terms a 0 , a 1 , ... ,an are the coefficients of the polynomial and need to be specified if the graph is to be drawn. If n = 1, 2, 3, 4, then we have respectively linear, quadratic, cubic and quartic functions of x. 1 Show that the minimum value of the function y occurs when x = 3. Now y x 2 - 6x + 9 (x - 3) 2 hence if x = 3, y = 0. Any other value we give to x has an associated value of y > 0 and so, when x = 0, y is a minimum. 7) L and p the power equal to 2.
2 g. are unknown constants. Check, by means of an appropriate graph, whether the model is reasonable for these data. Estimate by use of your graph a and k. 0 g? 7. 3 Graph these data and suggest an appropriate model. 8. The straight line y = a + Sx is known to pass through the points (1, -1) and (2,2), find a and S. What is the equation of the straight line parallel to the above and which passes through the point (2,7). Sketch these lines for values of x between -2 and +2. 9. Two points P and Q have co-ordinates (1, 2) and (3, 4), respectively.
Biomathematics: An Introduction by David Machin (auth.)