Limits And Continuities

Continuous

For the function to be continuous at a point, 2 conditions:

1. Limit must exist
2. ${\lim }_{x\to a}f(x)=f(a)$ This will always be try for continuous functions

Discontinuous

For the function to be discontinuous at a point, 2 conditions: $li{m}_{x\to a}f(x)\ne f(a)$ OR ${\lim }_{x\to a}f(x)DNE$ OR $L=\pm \infty ORf(x)=\pm \infty$ True for all discontinuous functions