Question

Did i do this correctly??

Answer 1

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

Answer 2

its just 1

Answer 3

then what does a say?

Answer 4

lim of f(x) as x approaches to 1

Answer 5

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

Answer 6

a is x->1-

Answer 7

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?

Answer 8

d doesn't exit because of the knot!

Answer 9

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

Answer 10

u mean the hole in the graph?

Answer 11

yes

Answer 12

so it does exist

Answer 13

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

Answer 14

so what about e?

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

kool!

Answer 19

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

Answer 20

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

Answer 21

like for b its undefined,

Answer 22

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

Answer 23

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

Answer 24

so a and b are both defined and c is undefined

Answer 25

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

Answer 26

does it means that the y value is 5?

Answer 27

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

Answer 28

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

Answer 29

so e) is 4

Answer 30

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

Answer 31

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

Answer 32

ohh okay got it now!

Answer 33

cool. so it doesn't exist, right?

Answer 34

no like u said coz of the hole!

Answer 35

yup :)

Answer 36

okay thanks for ur help guys!

Answer 37

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

Answer 38

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

Answer 39

yea i asked @phi if i did it right!

Answer 40

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

Answer 41

umm i could be wrong but i thought b exists

Answer 42

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

Answer 43

phi, u here?

Answer 44

umm okay

Answer 45

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

Answer 46

i m still confused on b!

Answer 47

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

Answer 48

2*

Answer 49

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

Answer 50

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

Answer 51

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

Answer 52

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

Answer 53

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

Answer 54

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

Answer 55

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

Answer 56

phi why do you think b doesn't exist?

Answer 57

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.

Answer 58

it is right to left. hmm

Answer 59

see the link, example 1

Answer 60

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

Answer 61

i agree!!

Answer 62

that's a really good tutorial tho

Answer 63

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

Answer 64

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

Answer 65

so yes, b is 3

Answer 66

Obviously I needed a refresher on this stuff.

Answer 67

alright so we all agree now b is 3!!

Answer 68

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

Answer 69

and yes, we agree

Answer 70

thanks all!!

Answer 71

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

Answer 72

yw!

Answer 73

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 :(

Answer 74

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

Answer 75

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

Answer 76

lol for real!! FAIL.. -_-

Answer 77

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

Answer 78

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

Answer 79

hmm but still. Stats is pretty much like math!