LIMITS FROM THE RIGHT AND LEFT

As we substitute values in for x we discover that the limit does not
exist because value of x<0 give us an f(x) of -1 and values of x>0 give us an
f(x) value of 1.

Remember the f(x) value is the limit not the x value!

However in some scientific and business situations we are only interested in
what the limit is as x approaches a number from one side.
So in the following limit, which is the
same as the one above, we are only going to use values of x > 0 and this will
give us what is called a limit from the right. So if you think of the number
line the values of x are to the right of zero and hence the name “limit from the
right”
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The limit f(x) is, according to the above chart, 1.
The limit from the left is written

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and in this case is -1