Mathematics
OpenStudy (liizzyliizz):

http://designatedderiver.wikispaces.com/file/view/GraphicalApproachLimits_IncludingInfinite.pdf find lim f(x) as x-> 1 from the left side graphically how do u do it?

OpenStudy (liizzyliizz):

i dont know how to do any of them. HELP

OpenStudy (anonymous):

wanna do example 1?

OpenStudy (liizzyliizz):

sure lol i need help with something, to start off ive done f9x)=1 but i dont know how to do the other 3. my teacher didnt bother teaching today so im kind of learning on my own -_-

OpenStudy (liizzyliizz):

f(x)*

OpenStudy (liizzyliizz):

wait that f(1) lol ive done that one silly me.

OpenStudy (anonymous):

ok example one. you want $\lim_{x\rightarrow 1^-}f(x)$ in english the limit as x goes to 1 from below

OpenStudy (anonymous):

hold on what did you get for each answer?

OpenStudy (liizzyliizz):

for f(1) i got 2. for the one u just wrote i think its 1. but im pretty sure its wrong... i dont know how to do it by just looking at the graph

OpenStudy (liizzyliizz):

i know when the dot is open it means theres a hole. but after that im a bit lost

OpenStudy (anonymous):

you have 4 questions. $f(1)$ is just one of them $f(1)=2$ because of the closed circle at (1,2)

OpenStudy (liizzyliizz):

yeah i only know how to do that one. the others im cofused in and the other examples with the vertical asymptotes freak me out lol

OpenStudy (anonymous):

$\lim_{x\rightarrow 1^-}f(x)=1$ because as you are walking left to right along the function headed towards x = 1 you are going up to y = 1

OpenStudy (anonymous):

$\lim_{x\rightarrow 1^+}f(x)=2$ because as you are walking along the function headed from right to left you are always at y = 2

OpenStudy (liizzyliizz):

wow i got them write. bbu i just guessed haha.. oh lord. what about the 3rd one? is it 1 as well

OpenStudy (anonymous):

$\lim_{x\rightarrow 1}f(x)$ does not exist because the limit from the left is 1, the limit from the right is 2 and they are not the same number!

OpenStudy (liizzyliizz):

oh ok. yeah i see

OpenStudy (liizzyliizz):

for example to would they be

OpenStudy (anonymous):

you can see that it is because the function has a "jump" there

OpenStudy (liizzyliizz):

yeah i see what u are saying. ok i did example 2 (thats as far as i got) but idk ill show u what i got

OpenStudy (anonymous):

#2$\lim_{x\rightarrow 1^-}f(x)=-1$

OpenStudy (anonymous):

$\lim_{x\rightarrow 1^+}f(x)=1$

OpenStudy (anonymous):

$\lim_{x\rightarrow 1}f(x)$again does not exist because those numbers are not the same

OpenStudy (anonymous):

and $f(1)=0$ because (1,0) is filled in

OpenStudy (anonymous):

OpenStudy (liizzyliizz):

ahh i did that one correct wow lol ok but when they have vertical asymptopes like example 7 and 8 how does that affect it/

OpenStudy (liizzyliizz):

example 3 would it be 1,1,1 and undef?

OpenStudy (liizzyliizz):

OpenStudy (anonymous):

yes you got it !

OpenStudy (anonymous):

example 4 is 1, 1, 1, -2

OpenStudy (anonymous):

example 5, 1, 1, 1, 1

OpenStudy (anonymous):

now we are ready for #6

OpenStudy (liizzyliizz):

omg im getting this lol :DDD now the asymptopes those guys i hesitated in.

OpenStudy (liizzyliizz):

OpenStudy (anonymous):

ok here we go $\lim_{x\rightarrow 2^-}f(x)=+\infty$

OpenStudy (anonymous):

or really we should say "does not exist" because infinity is not a number. but maybe you are supposed to say infinity. you are headed straight up

OpenStudy (anonymous):

typo sorry

OpenStudy (anonymous):

$\lim_{x\rightarrow 2^+}f(x)=-\infty$ because you are headed straight down

OpenStudy (liizzyliizz):

yeah the curve goes up and its continous, but im not sure what my teacher expects like i said she hasnt taught me anything she assumes i know this when i dont and it frustrayes me o.o so in those cases i would just put the infinity sign or DNE?

OpenStudy (anonymous):

and so $\lim_{x\rightarrow 2}f(x)$ does not exist. neither does $f(2)$

OpenStudy (anonymous):

really it is "dne" but you can put infinity to be on the safe side

OpenStudy (liizzyliizz):

the same would go for th the next problem?

OpenStudy (anonymous):

just make sure to put $\infty$ and $-\infty$ respectively

OpenStudy (liizzyliizz):

the*

OpenStudy (anonymous):

number 7 both limits are $\infty$

OpenStudy (anonymous):

since you are headed straight up. also $f(-2)$ does not exis

OpenStudy (anonymous):

*exist

OpenStudy (liizzyliizz):

for 8 f(-2) would be 0?

OpenStudy (liizzyliizz):

and the others

OpenStudy (anonymous):

ex 8 both limits are infinity but this time $f(-2)=0$ because of the closed circle at (-2,0)

OpenStudy (liizzyliizz):

$\infty$?

OpenStudy (anonymous):

yes you got this

OpenStudy (liizzyliizz):

im not going to lie, i learn better here then in my school. im not sure if thats bad or good?

OpenStudy (anonymous):

i was looking at examples, not homework right?

OpenStudy (liizzyliizz):

yeah those were examples. my actual hw looks much more complex lol

OpenStudy (liizzyliizz):

which is prob the next part of that link but i dont want you to do my hw for me, i want to learn it lol

OpenStudy (anonymous):

now don't be confused because $\lim_{x\rightarrow \infty}f(x)$ is different. this time you are looking as what happens as x gets bigger and bigger

OpenStudy (liizzyliizz):

oh ok

OpenStudy (liizzyliizz):

hmm for a on 1 it would be 1?

OpenStudy (anonymous):

example 9, infinity at both ends because the curve heads up

OpenStudy (anonymous):

are we on the homework now?

OpenStudy (liizzyliizz):

oh my packet didnt show an ex. 9 it stopped at 8. i was doing the hw as well while u were helping me with the examples.

OpenStudy (liizzyliizz):

yeah im at the hw now i just want to make sure im not letting go what u just taught me

OpenStudy (liizzyliizz):

a-d i got 1....

OpenStudy (anonymous):

homework 1 you got a)$\lim_{x\rightarrow 1^-}f(x)$ b) $\lim_{x\rightarrow 1^+}f(x)$ c) $\lim_{x\rightarrow 1}f(x)$ d)$f(1)$ e)$\lim_{x\rightarrow-\infty}f(x)$ f)$\lim_{x\rightarrow \infty}f(x)$

OpenStudy (liizzyliizz):

yes

OpenStudy (anonymous):

i might be looking at something different

OpenStudy (liizzyliizz):

the one with the closed dot at 1,1

OpenStudy (anonymous):

the one i am looking at a) limit from below is -2 b) limit from above is 2 c) limit from both sides does not exist

OpenStudy (anonymous):

yes d) f(1)=1

OpenStudy (liizzyliizz):

my bad yeah its cause you are looking at the y and i was paying more attention to the x.

OpenStudy (anonymous):

e) limit as you got to minus infinity is -2 since it is constant f) limit as you go to plus infinity is 2 for the same reason

OpenStudy (anonymous):

try 2 and tell me what you get. just write a) b) c) d) etc

OpenStudy (liizzyliizz):

kk :)

OpenStudy (liizzyliizz):

a)3 b)0 c)DNE d) 3 e)-2 f) i wasnt sure

OpenStudy (anonymous):

let me check

OpenStudy (liizzyliizz):

kk

OpenStudy (anonymous):

a,b,c, d are right

OpenStudy (anonymous):

it looks like as you go to minus infinity the curve is headed towards the x - axis where y = 0 so i think e) should be 0

OpenStudy (anonymous):

i think you were confused about e and f because looks like f should be -2

OpenStudy (anonymous):

looks like as x goes to positive infinity the curve is leveling out at y = -2

OpenStudy (liizzyliizz):

ok i guess i looked at it from the wrong end? lol ohh i was close i guess haha

OpenStudy (anonymous):

#3 is easier. i will let you do that one too. yah plus infinity is headed to the right, minus infinity to the left!

OpenStudy (liizzyliizz):

ok for 3 i got a) 1 b)1 c)1 d)1 e)-2 ? f) 3?

OpenStudy (anonymous):

ah you got them all but the infinity ones you are still confused about

OpenStudy (anonymous):

as x goes to minus infinity so does the function. trace your finger along the curve to the right and you will see it

OpenStudy (anonymous):

and as x goes to plus infinity so does the curve. it is headed up

OpenStudy (liizzyliizz):

aww :( i must be thinking too hard.... ok ill try that

OpenStudy (liizzyliizz):

f would be 4

OpenStudy (liizzyliizz):

and e -1.5?