Final answer:
If the one-sided portions of a limit do not match, it means that the limit does not exist. For example, in the function g(x) = 1/x, as x approaches 0 from the left side, the limit is negative infinity, while as x approaches 0 from the right side, the limit is positive infinity.
Step-by-step explanation:
If the one-sided portions of a limit do not match, it means that the limit does not exist.
Let's consider an example: Suppose we have the function f(x) = |x|. As x approaches 0 from the left side, the value of f(x) approaches 0. But as x approaches 0 from the right side, the value of f(x) also approaches 0. So, in this case, the one-sided portions of the limit match and the limit exists.
However, if we consider the function g(x) = 1/x, as x approaches 0 from the left side, g(x) approaches negative infinity, while as x approaches 0 from the right side, g(x) approaches positive infinity. In this case, the one-sided portions of the limit do not match, and we say that the limit does not exist.