Class notes APPM 1350 1.5

1.5 Continuity
A function f is continuous of x= α if Lithe f(x) = f(a).
a
Note: Polynomial, rational, and triforanchis functions are continuous on
each point in their donnainen. Algebrak Functions we continuous
on each interer point of their domains.
Lim
1. If xat fuss = f(a) then f is writinuous from the right
2 If him
xxa fox) = f(a) then it is continuous from the left
Consider continutity of fat:
lim
α) x = 1 Yes b/c xin f(x) = f(is
=
y= f(x)
a)
Oc If f is de ned on in
-1 fals
6) x = 3 f is continuous from the left
b/c his
I'm
fas=f(3) (f is not continuous
ble lim
x=3 f(x) ONE)
c) x=-2 t is not continuous from the lett
s
or night at x=-2
lim
an open interal in fox) does exist f(-2) does exist
but both must be equivalent
containing xea but possibly not at
x=a, and s not continues at xel,
then & has a discontinuity
Vati A discontinuity at x=a is:
ex cont. f has discontinuities
• a removable discontinuity if im f(x) exists
,a
jump
૪૨
at x=-2,~1,0,2
my discntinuity of I'm fcks and lia faxs both exist but
faxis are
-nequal
I'm
line
• an in nite discontinuity if im mit f(x) = 100 or kan man f(x) == 00
hemovable: x=2,-2 Jump: X=3 In nite: 0




fi fi fi fi fi fi