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.
To do
- Limits intro activity (Khan Academy)
- Limits by direct substitution activity (Khan Academy)
More info
- Introduction to limits quick tip (Study Support, USQ Library)
- Approaching limits (Study Support, USQ Library)
- Limits of functions more information sheet (mathcentre)
- Introduction to limits video (Khan Academy)
- Connecting limits and graphical behaviour (more examples) video (Khan Academy)