Method: Continuity Using an Equation

Step 1: Determine the overall limit, $\underset{x\to c}{\lim } f\left(x\right)$, at your given x-value .

Remember that you are now at the point where just finding the answer to a limit is just a step in the process. Here as a step, you need to be able to determine the overall limit of the equation. Hidden inside an overall limit question is always the need to determine your left-hand limit and your right-hand limit. By comparing the LHL and the RHL you are able to determine the overall limit.

Step 2: Determine the function value, $f\left(c\right)$, at your given x-value .

Step 3: Determine if the overall limit equals the function value, $\underset{x\to c}{\lim } f\left(x\right)=f\left(c\right)$.

–          If they are equal then the function is continuous at that x-value .

–          If they are not equal then the function is not continuous at that x-value .