Question

is 1/x continuous?

Answer 1

Is 1/x defined at all points?

Answer 2

not at zero?

Answer 3

no because limit f(x) x-> 0 != f(0)

Answer 4

So it isn't continuous.

Answer 5

Wait.

Answer 6

graph of 1/x

Answer 7

does that mean that sinx/x+1 isnt either?

Answer 8

yes

Answer 9

@ParthKohli maine bhi ek limit ka q pucha hai batado :3

Answer 10

Aapke questions nahi hotey :)

Answer 11

but if zero isnt in the domain doesnt some theorem say its only continuous for whats in its domain?

Answer 12

\[\lim _{x->0} \frac{ 1 }{ x } \neq \frac{ 1 }{ 0 }\]

Answer 13

Well, what I said was a loose explanation. Otherwise, use limits.

Answer 14

umm, ok i think

Answer 15

If the limit exists, yes, it is continuous.

Answer 16

a limit dies not define continuity ...

Answer 17

*does not define

Answer 18

hmm? I've always heard it that way, or that if you could draw the graph without lifting the pen.

Answer 19

the limit of a road that is approaching a bridge, would be the point defined by the bridge. The limit does not define if the bridge is there or not .....

Answer 20

take the function:

f(x) = x^2 for x not= 0
= 10 for x = 0

the limit exists at x=0, but it is not continuous at x=0

Answer 21

there also exists continuous functions that cannot be drawn; If memory serves, the direlicht function is such a monster

Answer 22

so if a function is not defined at a point, it's not continuous, right?

Answer 23

Of course

Answer 24

in general, that is a good way to see it. The continuity of a function has to be defined at a given point, and the limit at that point must be the same.

Answer 25

Thanks you! I was really misinformed here.

Answer 26

in my example; the limit as x to 0, f(x) to 0
but the value at x=0 is 10

since 0 not= 10, we have a discontinuity there