Question

having doubt plz help
lim x->0 [sin(abs(x))/x]

where abs is mod and [] denotes greatest function integer

for x-->0+ am getting 0
but for x-->0- how come it is -1

i know Limit won't exist getting it from 2nd method plz tell me
m confused
-_-

see limx->0- [-sinx/x] inside part should be lesser than 1 nah :O how come the value inside would be greater than 1 :O
if it greater than 1 then m getting answer but how it will be greater than 1 :'(
limx->0- [-sinx/x]

inside part sinx/x will be lesser than or greater than one ??????

Answer 1

Now let's right it as a piece-wise function:\[\bf \frac{\sin|x|}{x}=\frac{\sin(x)}{x} \ for \ x \ge0 \ and \ \frac{\sin(-x)}{x}=-\frac{\sin(x)}{x} \ for \ x < 0\]Evaluate the limit from the right and left sides:\[\bf \lim_{\ \ x \rightarrow 0^+}\frac{\sin|x|}{x}=\lim_{x \rightarrow 0}\frac{\sin(x)}{x}=1\]\[\bf \lim_{\ \ x \rightarrow 0^-}\frac{\sin|x|}{x}=\lim_{x \rightarrow 0}-\frac{\sin(x)}{x}=-1\]Clearly, the one-sided limits are unequal hence:\[\bf \lim_{x \rightarrow 0}\frac{\sin|x|}{x}=D.N.E\]

@kittycat01

Answer 2

huh ?
u have to take lhl and rhl nah
rhl m getting but having problem with lhl

Answer 3

wait that's u forgot to add greatest integer function

Answer 4

What are you talking about? @kittycat01

Answer 5

@genius12 -sinmod(x)/x is inside the greatest funtion interger bracket

Answer 6

grrrr plz help m still having doubt
thet floor bracket is confusing me :'(

Answer 7

oh thats greatest integer function lol i didnt notice that

Answer 8

:'(

Answer 9

who can help me :'(

Answer 10

http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=acc0a7e1a01e35f904fbdc148987612d&title=Limits%20Calculator&theme=blue&i0=floor%28sin%28abs%28x%29%29%2Fx%29&i1=x&i2=0&podSelect=&includepodid=Limit&podstate=Limit__Show%20steps&showAssumptions=1&showWarnings=1

Answer 11

:'(

Answer 12

@genius12 -do u know the answer ?
if no then no problem ,i m going to resolve it :)

Answer 13

https://www.desmos.com/calculator/4kbaskvfsp

Sorry I can't explain this, I have to leave.

@kittycat01

Answer 14

@genius12 -okay :)

Answer 15

observe the one-sided limits are different which you can find out without graphing the function, so the limit in this case also, does not exist. @kittycat01

Answer 16

@genius12
well i know limit won't exist but having difficulty in finding the value at lhl :)

Answer 17

for x->0 , sinx/x tends to 1-

Answer 18

but it's [sinx/x] nah :P

Answer 19

[1-] = 0
negative of this inside [ ] will make it -1 by the same logic

Answer 20

:/
[]=GIF
inside value is tending toward 1-
lt x-0- [-sin/x] =-2 :/

Answer 21

if m right then
lt n->0- [n] = n-1

Answer 22

*sorry n->a-

Answer 23

sin x /x = 0.999999 at x->0

[0.999999] = 0
[-0.99999]= -1

Answer 24

wait :OOOOOOOOOOOOO

Answer 25

let me think
let us take this one as a example
lt x->1- [-sinx/x]


-sinx/x = -0.854
so inside part would be tending towards 0-
so we will get -1 as a answer :/
now let us follow this for 0-
lt x->0-

sin(-0.1)/-0.1 =0.99

inner part is tending toward 0- so answer would be -1 -_-

Answer 26

oh :OOOOO i think now m getting it

Answer 27

grrr need more practise solving this type of questions -_-

Answer 28

hmm, practice will surely help :)
joshi sir se argument kiya karo, it'll help ^^

Answer 29

lol joshi sir toh pata nahi kaha hotai hai :P dikhtai hi nahi hai