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i can't quite read c is that x approaching 1-?
its just 1
then what does a say?
lim of f(x) as x approaches to 1
so its the same equation? a and c are both lim as x->1 of f(x)?
a is x->1-
oh ok. well yes A is correct. if b is x->x+ then it it is also correct, that limit does not exist. c is also correct, but d and e are incorrect...any idea why?
d doesn't exit because of the knot!
ohhh wait, but from the left hand and right hand side its meeting at 4
u mean the hole in the graph?
so it does exist
yep. f(5) doesn't have to be defined to have a limit there.. as long as it approaches the same number from both sides, it exists
so what about e?
wait ur 2nd last comment was on option d right!
well ya but i kind of gave away the answer to e, too, i think hah
but yes, for d, the limit as x->5 of f(x) exists because the function obviously approaches 4 at f(5).
so wht does it means if we hv a knot in the graph! why is it undef??
btw, the question asks for the value of the limit when it exists (not just that it exists)
like for b its undefined,
lol thanks @phi so u tell me if its right a) 2 b) 3 c) dne d) 4 e) dne
oh i'm sorry. ur right on b. that is defined since it's just coming from the right.
so a and b are both defined and c is undefined
d is also defined like we just talked about, but what about e?
does it means that the y value is 5?
well f(5) is asking what y is equal to when x=5
an open circle means that value is not defined. note that (e) is not a limit problem
so e) is 4
so if you look on the graph where x = 5, the there's a hole, meaning y is undefined
it basically skips over that one point. it approaches it from both sides, but y never equals 4 because theres that hole there
ohh okay got it now!
cool. so it doesn't exist, right?
no like u said coz of the hole!
okay thanks for ur help guys!
sure! the question also asks for the value of the quantity, if it exists
btw, if (b) is x-> 1+ (approaching from the right), the limit does not exist
yea i asked @phi if i did it right!
okay so a) 2 b) dne c) dne d) 4 e) dne, correct?
umm i could be wrong but i thought b exists
i actually wasn't sure so i looked it up, i'm seeing examples of limits approaching an undefined, discontinuous point from one side that exist
phi, u here?
but aside from that, i agree w ur answers, but i think b exists and it's 3
i m still confused on b!
coz from the left its 1 and it exist why it doesn't exist from the other side?
exactly...i think it does exist from the other side. i think phi's wrong
well i guess i hv to look for the difference btw the hole vs black hole!
definitely. black (filled in) means f(x) is defined at that point, hole (empty) means its not
there u go so it doesn't exist coz its empty
exactly. unless there's a black point somewhere randomly off the graph at the same x as the hole, then it's defined, just not continuous
do you have a link? see example http://tutorial.math.lamar.edu/Classes/CalcI/Continuity.aspx
idk if you've covered continuity yet, tho hah, so i don't want to add extra confusion.
phi why do you think b doesn't exist?
for(b) I can not read the problem, but if you are approaching x=1 from the left the limit defined. If you approach right to left, the limit is undefined.
it is right to left. hmm
see the link, example 1
in example 1 of the link, there's no mention of right-hand or left-hand limits...
that's a really good tutorial tho
I take it back. That first example was for continuity Here http://tutorial.math.lamar.edu/Classes/CalcI/OneSidedLimits.aspx example 4 , letters (f) and (g) show that one-sided limits exist. so (b) is 3
hah phew. I also first thought that b didn't exist haha but I checked and i was wrong.
so yes, b is 3
Obviously I needed a refresher on this stuff.
alright so we all agree now b is 3!!
i'm retaking calc 2 right now and am having to relearn everything after precalc, so i understand!
and yes, we agree
speaking of, phi, do you wanna try helping me with my own limit problem?
i've never used this site... but i really like teaching people so i'm enjoying it...even tho no one's even tried to answer my question :(
same here.. and ur question is kinda hard thts y nobody is willing to try!
lol my teacher's impossible! at the tutoring center in my college, sometimes professors come in and look at the problem and say, that's too hard, i dont want to help you with that
lol for real!! FAIL.. -_-
yup. not to me personally but it happened to my friend. the professor was like the dean of the math department, too haha
in his defense, tho, he's a stats guy, not calculus
hmm but still. Stats is pretty much like math!