The book Graphical Methods was written by author Carl Runge Here you can read free online of Graphical Methods book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Graphical Methods a good or bad book?
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On the f-scale we find 0.655, so that the third root is found equal to — 0.655. When b is negative there is always one and only one negative root. For 7i running through the values ?^ = to — oo, u^—h/u will run from — oo to + oo without turning. When h is positive there is always one and only one positive root; for then u^ — b/u GRAPHICAL REPRESENTATION OF FUNCTIONS. 47 runs from — oo to + oo for m = to + oo. In the first case there may be two positive roots or none; in the second case there ma...y be two negative roots or none. For positive values of a one root only exists in either case. This is easily seen in the first form of the equation V? -\- au = 6, because from a positive value of a it follows that u^ + clu will for w = — oo to + 00, run from — oo to + oo without turning and will therefore pass any given value once only. In order to decide whether in the case of a negative value of a there are three roots or only one let us write ?r — ^ = — o. u For negative values of h we have to investigate whether there are positive roots.
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