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What is a limit?

A limit is the value that a function, \(f(x)\), takes as the input, \(x\) "approaches" a specified value, \(a\). The limit is usually denoted \(\lim\), and is written as:
\[ \lim_{x\rightarrow a} f(x) = L \] The  above equation as read as "the limit of \(f\) of \(x\), as \(x\) approaches \(a\), is \(L\)” .

Methods of finding limits:

  • Use of the limit properties to allow direct substitution into the function.
  • Algebraically rearrange the function to allow the use of direct substitution.
  • Use a table or graph to infer the limit.