2. Let f be defined at each point of some open interval containing a, except possibly at a itself. Consider the statemen

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2 Let F Be Defined At Each Point Of Some Open Interval Containing A Except Possibly At A Itself Consider The Statemen 1 (365.13 KiB) Viewed 56 times

2. Let f be defined at each point of some open interval containing a, except possibly at a itself. Consider the statement: “For every 8 >0 there is an e > 0 such that if 0 < 12 - al <8, then f () - 11 < E." Show that this statement is not equivalent to the statement limete f(x) = L by letting f(x) = sin 1/x for 2 7 0 and a = 0. (Hint: For the special function f and a, which statement is valid, and which statement is not valid?)