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Question

The limit limx2x24x2  does not exist


  1. True

  2. False


Solution

The correct option is B

False


The limits we saw so far can be evaluated by direct substitution. If we substitute x=2 in the limit,

limx2x24x2  we will get 00. This does not mean that the limit does not exist, it means the value of the

function is not defined at that point. The expression x24x2 is equal to x+2 except at x=2. The graph of

x24x2 will look like

We can see that the function is not defined at x=2. But the value of  x24x2 approaches 4 as x approaches

2.We can say that the limit is 4.

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