Page 6 - Calc for the Clueless

Example 4—

Example 5—

which is undefined.

The limit does not exist. The limit must be a number; infinity is not a number.

Let's give one more demonstrated example of what it is to find the limit point by point.

First we let x = 2. We find the answer is 0/0. Let's make charts again.

x x

3 1.0 1 0.6

2.5 0.9 1.5 0.7

2.1 0.82 1.9 0.78

2.01 0.802 1.99 0.798

2.001 0.8002 1.999 0.7998

So

and

1

Therefore, the limit is 0.8. However, we can't make a chart every time. For Examples 3, 4, and 5, a chart is not
necessary. However, Example 6 shows what has to be done sometimes.

Warning: Substitution of a number like x = 2 does not work all the time, especially when you have a function
that is defined in pieces, such as that in Example 21 at the end of this chapter. Note that f(1) = 6, but