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# Limits

### 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.