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limits - Suppose(x is a real-valued function and c is a...

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Suppose ƒ( x ) is a real-valued function and c is a real number. The expression: means that ƒ( x ) can be made to be as close to L as desired by making x sufficiently close to c . In that case, we say that "the limit of ƒ of x , as x approaches c , is L ". Note that this statement can be true even if . Indeed, the function ƒ( x ) need not even be defined at c . Two examples help illustrate this. Consider as x approaches 2. In this case, f ( x ) is defined at 2 and equals its limit of 0.4: f (1.9) f (1.99) f (1.999) f (2) f (2.001) f (2.01) f (2.1) 0.4121 0.4012 0.4001 0.4 0.3998 0.3988 0.3882
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