Question

Suppose lim (as x approaches 0-) f(x)=3 and lim (as x approaches 0+) f(x)=4. What happens in the graph of f when x = 0?

Answer 1

@xapproachesinfinity

Answer 2

@Loser66

Answer 3

@caozeyuan

Answer 4

old man knows the answer :)

Answer 5

hehehe, i will try ;(

Answer 6

Who is old man?? :P

Answer 7

f is discontinued at 0

Answer 8

that's what they want you to realize

Answer 9

do you want me to explain it further?

Answer 10

yes, please.

Answer 11

Yes please:)

Answer 12

ok,
we are given \[\lim_{x\to 0^-}f(x)=3~~and~~ \lim_{x\to 0^+}f(x)=4\]
Hence \[\lim_{x\to 0^-}f(x) \ne\lim_{x\to 0^+}f(x)\]
then, \[\lim_{x\to 0}f(x) ~~~does~not~exist\]
it reasonable then to say that f is not continuous at 0

Answer 13

Ohhhh I get it! Thank you! :)

Answer 14

recall the continuity def:
let f be a function from R to R
f is said to be continuous at x0 if and only if the three condition meet:
1) f(x0) exist
2) \lim f(x) exist as x goes to x0
3) lim f(x)=f(x0)

Answer 15

np!

Answer 16

Woah!! kid is the best. :)
graphing it, please.

Answer 17

suppose this to be our function y=f(x)

Answer 18

xapproachesinfinity you're the best! :)

Answer 19

you can see the jump, which indicates the discontinuity

Answer 20

thanks :)

Answer 21

it just about understanding the concepts, definitions

Answer 22

good luck :)

Answer 23

Thanks again! :)