Question

Suppose that lim(x->4-) f(x)=8, and that f (4) is undefined.
  a. Write a limit statement so that there is a removable discontinuity at x=4 .
b. Write a limit statement so that there is a jump discontinuity at x= 4.

Answer 1

the (x->4-) should be under the lim

Answer 2

Please EXPLAIN if u know how to do it

Answer 3

are you ok with that?

Answer 4

answer and ill continue

Answer 5

a bit confused..i already have the answer but I just don't know how to get to it

Answer 6

what I drew means the limit when x tends to FOUR at the LEFT, from the left, you can also take the limit from the right

Answer 7

4- is not MINUS FOUR, it's 4 FROM LEFT, and 4+ is not PLUS FOUR it's 4 from the right

Answer 8

oh Ok..so how u can write a removal discontinuity and a jump discontinuity from what you're already given

Answer 9

you need a function first, that's why im thinking this is a weird exercise

Answer 10

i can teach you how to take limits, what's continuity about and how to know what kind of discontinuity is each one

Answer 11

i think it means f(4) does not exist, but I'm not sure

Answer 12

maybe you can tell me how did you get the solution and we see it

Answer 13

ok the answer for the first one was lim(x->4+) f(x)=8 but I have no idea where the 8 came from

Answer 14

exactly lmao, where's the f(x)?

Answer 15

if lim x->4- of f(x) is 8

Answer 16

and then the lim when x tents to 4- is 8 as well

Answer 17

then it means the function is CONTINUOUS in that point, x=4

Answer 18

because its sidewards limits have the same value

Answer 19

if for example if lim x-4+ of f(x) = 8 and then lim x -4- of f(x) was for example 5, then the function won't be continuous and would have a finite jump discontinuity

Answer 20

if lim x-4+ of f(x) = 8 and lim of f(x) = INIFINITE, then it would be an infinite jump discontinuity

Answer 21

how you doing?

Answer 22

it's a property you have to learn very well, if the sidewards limits of a function have the same, then it's continuous at that point (except if it gives you INIFINITE ofc, there's no point "INFINITY" in the real line)

Answer 23

have the same value*

Answer 24

ok I got some things u said..but i felt like u were talking in another language when explaining the property ( I don't remember learning about it.) Thanks for the help though! :)

Answer 25

I think you need to get limits explained very well before going into that kind of exercises, they are not hard, but you need to know 3 things VERY WELL

Answer 26

what do you know of limits?

Answer 27

alright..i'll just try watching some Youtube vids about it or something since my teacher never explains this stuff too well.

Answer 28

That's a big problem for people who actually wants to learn, I know it...

Answer 29

a concept you need to have always in your head when talking about limits is its meaning

Answer 30

Do you really know what does lim x-1 means?

Answer 31

excuse me if I seem anoying, I like to explain things as simple as possible.

Answer 32

no it's cool..does it mean that it's approaching 1 from the left side?

Answer 33

I mean a more deep meaning

Answer 34

a mathematical meaning,

Answer 35

the mathematical concept of limits means that the limit approaches really really really really close, but never gets to the point, that's why we say "tend".