A function f$($x$)$f$($x$)$ is said to have a jump discontinuity at x$=$ax$=$a if:

$1.$ limx$$a$$f$($x$)$limx$$a$-$f$($x$)$ exists.

$2.$ limx$$a$+$f$($x$)$limx$$a$+$f$($x$)$ exists.

$3.$ The left and right limits are not equal.

Let f$($x$)=\{5$x$5$ifx$<91$x$+6$ifx$9$f$($x$)=\{5$x$-5$ifx$<91$x$+6$ifx$9$

Show that f$($x$)$f$($x$)$ has a jump discontinuity at x$=9$x$=9$ by calculating the limits from the left and right at x$=9$x$=9.$

limx$9$f$($x$)=$limx$9-$f$($x$)=40$Correct $$

limx$9+$f$($x$)=$limx$9+$f$($x$)=559$Incorrect $$