math456
Did i do this correctly??
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math456
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jldstuff393
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i can't quite read c is that x approaching 1-?
math456
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its just 1
jldstuff393
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then what does a say?
math456
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lim of f(x) as x approaches to 1
jldstuff393
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so its the same equation? a and c are both lim as x->1 of f(x)?
math456
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a is x->1-
jldstuff393
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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?
math456
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d doesn't exit because of the knot!
math456
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ohhh wait, but from the left hand and right hand side its meeting at 4
jldstuff393
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u mean the hole in the graph?
jldstuff393
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yes
math456
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so it does exist
jldstuff393
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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
jldstuff393
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so what about e?
math456
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wait ur 2nd last comment was on option d right!
jldstuff393
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well ya but i kind of gave away the answer to e, too, i think hah
jldstuff393
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but yes, for d, the limit as x->5 of f(x) exists because the function obviously approaches 4 at f(5).
math456
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kool!
math456
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so wht does it means if we hv a knot in the graph! why is it undef??
phi
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btw, the question asks for the value of the limit when it exists (not just that it exists)
math456
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like for b its undefined,
math456
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lol thanks @phi so u tell me if its right a) 2 b) 3 c) dne d) 4 e) dne
jldstuff393
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oh i'm sorry. ur right on b. that is defined since it's just coming from the right.
jldstuff393
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so a and b are both defined and c is undefined
jldstuff393
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d is also defined like we just talked about, but what about e?
math456
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does it means that the y value is 5?
jldstuff393
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well f(5) is asking what y is equal to when x=5
phi
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an open circle means that value is not defined.
note that (e) is not a limit problem
math456
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so e) is 4
jldstuff393
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so if you look on the graph where x = 5, the there's a hole, meaning y is undefined
jldstuff393
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it basically skips over that one point. it approaches it from both sides, but y never equals 4 because theres that hole there
math456
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ohh okay got it now!
jldstuff393
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cool. so it doesn't exist, right?
math456
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no like u said coz of the hole!
jldstuff393
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yup :)
math456
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okay thanks for ur help guys!
jldstuff393
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sure! the question also asks for the value of the quantity, if it exists
phi
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btw, if (b) is x-> 1+ (approaching from the right), the limit does not exist
math456
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yea i asked @phi if i did it right!
math456
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okay so a) 2 b) dne c) dne d) 4 e) dne, correct?
jldstuff393
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umm i could be wrong but i thought b exists
jldstuff393
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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
jldstuff393
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phi, u here?
math456
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umm okay
jldstuff393
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but aside from that, i agree w ur answers, but i think b exists and it's 3
math456
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i m still confused on b!
math456
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coz from the left its 1 and it exist why it doesn't exist from the other side?
math456
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2*
jldstuff393
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exactly...i think it does exist from the other side. i think phi's wrong
math456
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well i guess i hv to look for the difference btw the hole vs black hole!
jldstuff393
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definitely. black (filled in) means f(x) is defined at that point, hole (empty) means its not
math456
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there u go so it doesn't exist coz its empty
jldstuff393
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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
jldstuff393
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idk if you've covered continuity yet, tho hah, so i don't want to add extra confusion.
jldstuff393
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phi why do you think b doesn't exist?
phi
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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.
jldstuff393
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it is right to left. hmm
phi
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see the link, example 1
jldstuff393
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in example 1 of the link, there's no mention of right-hand or left-hand limits...
math456
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i agree!!
jldstuff393
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that's a really good tutorial tho
jldstuff393
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hah phew. I also first thought that b didn't exist haha but I checked and i was wrong.
jldstuff393
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so yes, b is 3
phi
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Obviously I needed a refresher on this stuff.
math456
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alright so we all agree now b is 3!!
jldstuff393
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i'm retaking calc 2 right now and am having to relearn everything after precalc, so i understand!
jldstuff393
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and yes, we agree
math456
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thanks all!!
jldstuff393
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speaking of, phi, do you wanna try helping me with my own limit problem?
jldstuff393
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yw!
jldstuff393
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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 :(
math456
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same here.. and ur question is kinda hard thts y nobody is willing to try!
jldstuff393
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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
math456
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lol for real!! FAIL.. -_-
jldstuff393
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yup. not to me personally but it happened to my friend. the professor was like the dean of the math department, too haha
jldstuff393
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in his defense, tho, he's a stats guy, not calculus
math456
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hmm but still. Stats is pretty much like math!