- anonymous

Did i do this correctly??

- katieb

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- anonymous

##### 1 Attachment

- anonymous

i can't quite read c is that x approaching 1-?

- anonymous

its just 1

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## More answers

- anonymous

then what does a say?

- anonymous

lim of f(x) as x approaches to 1

- anonymous

so its the same equation? a and c are both lim as x->1 of f(x)?

- anonymous

a is x->1-

- anonymous

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?

- anonymous

d doesn't exit because of the knot!

- anonymous

ohhh wait, but from the left hand and right hand side its meeting at 4

- anonymous

u mean the hole in the graph?

- anonymous

yes

- anonymous

so it does exist

- anonymous

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

- anonymous

so what about e?

- anonymous

wait ur 2nd last comment was on option d right!

- anonymous

well ya but i kind of gave away the answer to e, too, i think hah

- anonymous

but yes, for d, the limit as x->5 of f(x) exists because the function obviously approaches 4 at f(5).

- anonymous

kool!

- anonymous

so wht does it means if we hv a knot in the graph! why is it undef??

- phi

btw, the question asks for the value of the limit when it exists (not just that it exists)

- anonymous

like for b its undefined,

- anonymous

lol thanks @phi so u tell me if its right a) 2 b) 3 c) dne d) 4 e) dne

- anonymous

oh i'm sorry. ur right on b. that is defined since it's just coming from the right.

- anonymous

so a and b are both defined and c is undefined

- anonymous

d is also defined like we just talked about, but what about e?

- anonymous

does it means that the y value is 5?

- anonymous

well f(5) is asking what y is equal to when x=5

- phi

an open circle means that value is not defined.
note that (e) is not a limit problem

- anonymous

so e) is 4

- anonymous

so if you look on the graph where x = 5, the there's a hole, meaning y is undefined

- anonymous

it basically skips over that one point. it approaches it from both sides, but y never equals 4 because theres that hole there

- anonymous

ohh okay got it now!

- anonymous

cool. so it doesn't exist, right?

- anonymous

no like u said coz of the hole!

- anonymous

yup :)

- anonymous

okay thanks for ur help guys!

- anonymous

sure! the question also asks for the value of the quantity, if it exists

- phi

btw, if (b) is x-> 1+ (approaching from the right), the limit does not exist

- anonymous

yea i asked @phi if i did it right!

- anonymous

okay so a) 2 b) dne c) dne d) 4 e) dne, correct?

- anonymous

umm i could be wrong but i thought b exists

- anonymous

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

- anonymous

phi, u here?

- anonymous

umm okay

- anonymous

but aside from that, i agree w ur answers, but i think b exists and it's 3

- anonymous

i m still confused on b!

- anonymous

coz from the left its 1 and it exist why it doesn't exist from the other side?

- anonymous

2*

- anonymous

exactly...i think it does exist from the other side. i think phi's wrong

- anonymous

well i guess i hv to look for the difference btw the hole vs black hole!

- anonymous

definitely. black (filled in) means f(x) is defined at that point, hole (empty) means its not

- anonymous

there u go so it doesn't exist coz its empty

- anonymous

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

- phi

do you have a link?
see example
http://tutorial.math.lamar.edu/Classes/CalcI/Continuity.aspx

- anonymous

idk if you've covered continuity yet, tho hah, so i don't want to add extra confusion.

- anonymous

phi why do you think b doesn't exist?

- phi

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.

- anonymous

it is right to left. hmm

- phi

see the link, example 1

- anonymous

in example 1 of the link, there's no mention of right-hand or left-hand limits...

- anonymous

i agree!!

- anonymous

that's a really good tutorial tho

- phi

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

- anonymous

hah phew. I also first thought that b didn't exist haha but I checked and i was wrong.

- anonymous

so yes, b is 3

- phi

Obviously I needed a refresher on this stuff.

- anonymous

alright so we all agree now b is 3!!

- anonymous

i'm retaking calc 2 right now and am having to relearn everything after precalc, so i understand!

- anonymous

and yes, we agree

- anonymous

thanks all!!

- anonymous

speaking of, phi, do you wanna try helping me with my own limit problem?

- anonymous

yw!

- anonymous

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 :(

- anonymous

same here.. and ur question is kinda hard thts y nobody is willing to try!

- anonymous

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

- anonymous

lol for real!! FAIL.. -_-

- anonymous

yup. not to me personally but it happened to my friend. the professor was like the dean of the math department, too haha

- anonymous

in his defense, tho, he's a stats guy, not calculus

- anonymous

hmm but still. Stats is pretty much like math!

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