A function
f(x)
is said to have a jump discontinuity at
x=a
if:
\lim_(x->a^(-))f(x)
exists.
\lim_(x->a^(+))f(x)
exists. The left and right limits are not equal. Let
f(x)={(8x-5, if x<9),((1)/(x+9), if x>=9):}
Show that
f(x)
has a jump discontinuity at
x=9
by calculating the limits from the left and right at
x=9
.
\lim_(x->9^(-))f(x)=
\lim_(x->9^(+))f(x)=
Now, for fun, try to graph
f(x)
.