Byju's Limit Calculator is a tool which makes calculations very simple and interesting.
If an input is given then it can easily show the result for the given number.
Factoring this one is just a little harder, but the idea is exactly the same.
\begin \lim_\dfrac &= \text \\ \\ &= \lim_\dfrac \\ \\ &= \lim_\dfrac \\ \\ &= \lim_[x 1] \\ \\ &= 6 \quad \cmark\end You probably have some problems that look like $$\lim_ \dfrac = ?
Instead, there’s probably a polynomial you can expand.
For example, here’s a problem a student asked us via Twitter:$$\lim_\dfrac = ?
Textbooks are good sources of graphs showing continuous and discontinuous functions.
If you have a smartboard you may want to try an online interactive gallery for graphing functions which can be found at: Maths Online from the University of Vienna, Austria.
From the left and right side of the limiting x value 2, the y value is approaching -4. If the result of direct substitution results in a function that is 0/0, the answer is undefined at this point, yet the limit still exists.
To evaluate the limits students need to be shown several examples.