Question

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?

Answer 1

i dont know how to do any of them. HELP

Answer 2

wanna do example 1?

Answer 3

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 -_-

Answer 4

f(x)*

Answer 5

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

Answer 6

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

Answer 7

hold on what did you get for each answer?

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

oh ok. yeah i see

Answer 17

for example to would they be

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

ready for #3?

Answer 25

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/

Answer 26

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

Answer 27

yeah im ready lol

Answer 28

yes you got it !

Answer 29

example 4 is 1, 1, 1, -2

Answer 30

example 5,
1, 1, 1, 1

Answer 31

now we are ready for #6

Answer 32

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

Answer 33

yeah im ready

Answer 34

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

Answer 35

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

Answer 36

typo sorry

Answer 37

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

Answer 38

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?

Answer 39

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

Answer 40

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

Answer 41

the same would go for th the next problem?

Answer 42

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

Answer 43

the*

Answer 44

number 7 both limits are
\[\infty\]

Answer 45

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

Answer 46

*exist

Answer 47

for 8 f(-2) would be 0?

Answer 48

and the others

Answer 49

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

Answer 50

\[\infty\]?

Answer 51

yes you got this

Answer 52

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

Answer 53

i was looking at examples, not homework right?

Answer 54

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

Answer 55

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

Answer 56

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

Answer 57

oh ok

Answer 58

hmm for a on 1 it would be 1?

Answer 59

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

Answer 60

are we on the homework now?

Answer 61

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.

Answer 62

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

Answer 63

a-d i got 1....

Answer 64

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

Answer 65

yes

Answer 66

i might be looking at something different

Answer 67

the one with the closed dot at 1,1

Answer 68

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

Answer 69

yes
d) f(1)=1

Answer 70

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

Answer 71

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

Answer 72

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

Answer 73

kk :)

Answer 74

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

Answer 75

let me check

Answer 76

kk

Answer 77

a,b,c, d are right

Answer 78

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

Answer 79

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

Answer 80

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

Answer 81

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

Answer 82

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

Answer 83

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

Answer 84

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

Answer 85

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

Answer 86

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

Answer 87

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

Answer 88

f would be 4

Answer 89

and e -1.5?