Limit of a Function

The number 1Lis said to be the left-hand limit of as x approaches a. Similarly, if can be made arbitrarily close to a number L 2 by taking xsufficiently close to, but not equal to, a num- ber a from the right, then L 2 is the right-hand limit of as approaches x a and we write (4) The quantities in (3) and (4) are also referred to as one-sided limits. Two-Sided LimitsIf both the left-hand ... ................
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