At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
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,
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
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!