Question

Prove that the function "the sign of x" y=sgnx,such that sgnx={1 for x>0
{0 for x=0
{-1 for x<0 has no limit at the point where x=0.

Answer 1

Can you help me please? @amistre64 @Michele_Laino

Answer 2

what defines a limit?

Answer 3

the lim f(x) as x approaches to 0

Answer 4

not quite, its more precise than that

Answer 5

if something is there, then we should be able to get there no matter which direction we come from.

if we reach the same place fro any direction, then the limit is the place that everything converges to.

Answer 6

i guess *as x approaches to 0

Answer 7

since we are limited by the direction of x, we have 2 ways to approach f(a) at a

Answer 8

what is the limit as x approaches 0 from the left? from the right? is it the same?

Answer 9

what is lim f(0) as x approaches from the left?

f(-1), f(-.5), f(-.25), f(-.0025), ....
--------------------------

what is lim f(0) as x approaches from the right?

f(1), f(.5), f(.25), f(.0025), ....
---------------------------

do lims of f(0) match from the left and from the right?

Answer 10

I didn't get it ! @amistre64

Answer 11

"Prove" suggests you have to use the \(\epsilon-\delta\) definition, but that depends on whether @M_lowreen has learned about that.

Answer 12

what's that ? @SithsAndGiggles

Answer 13

what are the values for:

f(-1), f(-.5), f(-.25), f(-.0025)?



what are the values for:

f(1), f(.5), f(.25), f(.0025)?

Answer 14

@M_lowreen it's the rigorous way of proving that a limit exists. If you haven't learned it yet, don't worry about it.

Answer 15

graphing the function might help ... and knowing how your material defines this limiting process would be good.

Answer 16

we r given that sgnx=1for x>0 , sgnx=0 for x=0 and sgnx=-1 for x<0 that's all we know , how can i graph it !? @amistre64

Answer 17

by following the definition

how do you graph something like f(x) = x?

Answer 18

start with the xy axises ... and

where x is < 0 draw the line y=-1
where x is > 0 draw the line y=
where x is = 0 make a point at y=0

Answer 19

we give some values to the x and find f(x) ... but we have not f(x)=... it's sgnx=

Answer 20

f(x) is a name, a generic name

sgn(x) is a name, a specific name

Answer 21

you simply draw out the rule that defines it