# 2.2 Limit of a Function and Limit Laws.pdf - 2.2 Limit of a...

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2.2 Limit of a Function and Limit Laws Consider the function f ( x ) = x 2 - 4 x + 2 . f is undefined at x = - 2 . Question: What happens to the value of f ( x ) if x gets nearer and nearer to - 2 , without touching - 2 itself?
Definition 1 (Limit) . We say that "the limit f ( x ) , as x approaches a , equals L " and write lim x a f ( x ) = L if the value f ( x ) can be made arbitrarily close to L for all x sufficiently near a on either side of a , but x 6 = a . Definition of Limit of a Function Alternate notation of limit is to write f ( x ) L as x a That is, f ( x ) approaches L as x approaches a . Example 1 . From the graph below, find lim x →- 1 f ( x ) , lim x 0 f ( x ) , lim x 1 f ( x ) , and lim x 3 f ( x ) . 1