- Examples%%visits: 3 ## introduction ## intuition
Point discontinuity can be less obvious than the others.
Point discontinuity:~ This is where left limit = right limit but “centre” point is not defined, so it continuous at a point but not continuous at an interval.
removable discontinuit := Point discontinuity :~ both
left and right limit at x0 exist, and they are
the same, but the point x0 is not the same, e.g
y = x2
with x = 0, y = 5
jump discontinuit := both limits exist but they are not
equal to each other :~ the is a jump in the graph.
Infinite discontinuit := 1 of the left or right limits
are infinite, e.g. $f(x)=\frac{1}{x}$
at x = 0
Oscillatory discontinuit := at least one of the limits
do not exist. e.g. $\sin \left( \frac{1}{x}
\right)$ ## rigour ## exam clinic ## resources tags :math: