2.13 Limits

If there exists a real number $L$ such that $f(x)$ gets close to $L$ whenever $x$ tends to $b$, then we call $L$ the limit and write

The full definition of this is given in MATH 113. Note that $x$ does not equal $b$, although $x$ is close to $b$; further, $f(x)$ may never be equal to $L$. In this notation, $b$ and $L$ are fixed; whereas $x$ and $f(x)$ vary. It is not good to confuse the notation by writing $\lim_{x\rightarrow b}f(x)\rightarrow L.$