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?

i dont know how to do any of them. HELP

wanna do example 1?

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 -_-

f(x)*

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

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

hold on what did you get for each answer?

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

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

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

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

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

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

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

\[\lim_{x\rightarrow 1}f(x)\] 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!

oh ok. yeah i see

for example to would they be

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

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

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

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

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

and \[f(1)=0\] because (1,0) is filled in

ready for #3?

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/

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

yeah im ready lol

yes you got it !

example 4 is 1, 1, 1, -2

example 5, 1, 1, 1, 1

now we are ready for #6

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

yeah im ready

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

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

typo sorry

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

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?

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

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

the same would go for th the next problem?

just make sure to put \[\infty\] and \[-\infty\] respectively

the*

number 7 both limits are \[\infty\]

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

*exist

for 8 f(-2) would be 0?

and the others

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

\[\infty\]?

yes you got this

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

i was looking at examples, not homework right?

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

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

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

oh ok

hmm for a on 1 it would be 1?

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

are we on the homework now?

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.

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

a-d i got 1....

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)\[\lim_{x\rightarrow \infty}f(x)\]

yes

i might be looking at something different

the one with the closed dot at 1,1

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

yes d) f(1)=1

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

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

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

kk :)

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

let me check

kk

a,b,c, d are right

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

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

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

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

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

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

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

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

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

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

f would be 4

and e -1.5?

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