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-oo if, given there is X such that f(x) -11 < e for all x < - X. There is a further limit situation which does not occur for sequences s , but which presents itself for functions of x. To exemplify it, consider 1 E, , Y x-2" As x approaches 2, taking values greater than 2, y oo.

Such that'. ' In this book symbolism of this kind will be used from time to time, but not on every possible occasion. It is the experience of many students of mathematics that arguments are easier to follow if brevity is not made the prime consideration and if symbolic statements are relieved by verbal sentences. 3 (5) You may find that a graphical representation helps to clarify the notion of limit. , the y-coordinate of the nth point being sn. Draw the line y = s and the parallel lines y = s e and y = s+e; the part of the plane between these parallels forms a band of width 2e.

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A First Course in Mathematical Analysis by J. C. Burkill


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