By Charles L. Dodgson

ISBN-10: 141817985X

ISBN-13: 9781418179854

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**Extra info for An elementary treatise on determinants**

**Example text**

7 x Fig. J x I' and analyze another interesting question, using this example. Let us try to find the highest point of the right half of the graph, exactly (and, hence, also the lowest point of the left half). Obviously, our curve cannot rise very high, because the denominator x 2 + I starts quite rapidly to outgrow the numerator x. 'le curve can reach a height equal to I, that is, whether for some x, the value of y can be equal to I. Since y = x/(x 2 + I), it is necessary to solve the equation x/(x 2 + I) or the equation x 2 - x + I = O.

Xs-l 2. I" I I I I It is already in the form of the sum of two functions, 1. Prove the inequality x I + -x> 2 for x > 0 (1) directly. 2. Prove the inequality and of course it is possible to construct its graph by addingthegraphsofy= I/(x+ I)andy= I/(x-I). " Inequality I is a particular case of Inequality 2. For what a and b? 3. " An honest merchant knew that the scales on which he was weighing his merchandise were inaccurate, because one beam was somewhat longer than the other (at that time they were still using scales as shown in Fig.

Check that the graph of y EXERCISE Find the largest ordinate of the graph of y (x - I)/(x 1)2 (see Chapter 2). + = H let us construct the graph of the function 2 + x I y=-x-' ·Was it mere coincidence that a complete square was ob· tained? 84 Fig. 13 = (x 2 + I)/x is symmetric with respect to the origin. 2. Find the coordinates of the lowest point of the right-hand branch of the graph of y = (x 2 + I)/x. The answer to the second exercise is clear from the first method by which this graph was constructed (see Fig.

### An elementary treatise on determinants by Charles L. Dodgson

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