A function f(x) is said to have a jump discontinuity at x = a if: 1. lim f(x) exists. x→a 2. lim f(x) exists. a+ 3. The left and right limits are not equal. 4, if x < 9 if x ≥ 9 8x Let f(x)= = 2 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 f(x): lim f(x) = x 9+ Now, for fun, try to graph f(x).

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
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A function f(x) is said to have a jump discontinuity at x = a if:
1. lim f(x) exists.
_D-X
2. lim f(x) exists.
x→a+
3. The left and right limits are not equal.
Let f(x)
18x-4, if x <9
if x > 9
2
(
x+99
Show that f(x) has a jump discontinuity at
lim f(x)
x→9-
lim f(x)
x→9+
Now, for fun, try to graph f(x).
=
9 by calculating the limits from the left and right at x = છે.
Transcribed Image Text:A function f(x) is said to have a jump discontinuity at x = a if: 1. lim f(x) exists. _D-X 2. lim f(x) exists. x→a+ 3. The left and right limits are not equal. Let f(x) 18x-4, if x <9 if x > 9 2 ( x+99 Show that f(x) has a jump discontinuity at lim f(x) x→9- lim f(x) x→9+ Now, for fun, try to graph f(x). = 9 by calculating the limits from the left and right at x = છે.
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