i got discontinuity at x=-1, x=0, x=1
removeable at x=1, jump at x=-1, is it infinite at x=0?
and my reasoning behind x=1 was that a limit from the left and right as x-> 1 exists and a limit exists but since there is a hole at (1,1) f(1) does not exist therefore it is a removeable discontinuity
reasoning behind x=1 was that limit from the left and right were not equal and a limit does not exist when x-> -1
which produces jump discontinuity
idk how 2 prove infinite discontinuity tho or if that even is an infinite discontiunity or if its a jump
cuz its not like all the infinite discontinuities i've seen where the limit from left and right is infinitely approaching 0
from the left it's infinitely approaching 0 but from the right it's going towards a hole at like roughly (0,3)
so if anyone could double check my reasoning and answers for x=1 and x=-1 as well as explain to me x=0 i'd appreciate it 🫡
#calc 1 discontinuity help
fading blade
wind pelicanBOT
knotty idol
Yeah X=1 and -1 look good
fading blade
ok cool n then x=0
knotty idol
And for an infinite discontinuity if the limit doesn’t exist for either side
knotty idol
Nah from the left as X approaches 0
Y approaches infinity
So the limit doesn’t exist
So it’s an infinite discontinuity
fading blade
because there's no limit from the left side
and none from the right side because of the hole?
knotty idol
Yeah for the first one
knotty idol
and none from the right side because of the hole?
From the right it approaches 3
Limits is like saying what does it get close to
So since from the right it gets close to 3
The limit from the right is three
But from the left since it goes to infinity it doesn’t get close to anything so there is no limit
fading blade
so it would be the top one
these were the notes i took for each discontinuity
i didnt get any for infinite and i dont really get what i wrote for removeable
knotty idol
Both are right
Like the names are kind of intuitive
Removable is like you grab the point and put it somewhere else
fading blade
is there like a clear set of conditions somewhere for each discontinuity using the formal definition if discontinutiy 😔
knotty idol
Hence you “remove” it
A jump is well where you jump XD
And infinite is where one of the limits is infinity
fading blade
ok so for x=0 its an infinite discontinutiy because when takign the limit from the left we're given infinity which means it is an infinite discontinuity
knotty idol
This is pretty good honestly with some examples
knotty idol
ok so for x=0 its an infinite discontinutiy because when takign the limit from t...
Yeah
fading blade
so whenever i get limit = plus or minus infinity/DNE then its infinite discontinutiy
removeable happens when i get uh
a limit exists but L does NOT equal f(x)
and jump happens when the limit from left and right differ therefore lim f(x) doesnt exist
that sound right?
knotty idol
Yeah that sounds awesome
fading blade
sweet ty
knotty idol
You’re welcome mate have a good one
fading blade
u2
stiff granite
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