Question

CONTINUITY QUESTION :
Examine the continuity of the function :
f(x)= ( 2[x] )/ ( 3x-|x| ) at x=-1/2 and x=1

Answer 1

In order to get the best possible answers, it is helpful if you say in what your thoughts on it are so far; this will prevent people from telling you things you already know, and help them write their answers at an appropriate level.

Answer 2

Well said @FoolForMath ! :p

Answer 3

I know, I am so amazing ;)

Answer 4

Oh please ! WAKE UP ! :P

Answer 5

Anyways , I will believe that you are SUPER-DUPER AMAZING , only when you will SOLVE THIS question ! :p And please no direct answers , the whole explanation is required :p

Answer 6

who said I need your credence? :P

Answer 7

A FRIEND IN NEED IS A FRIEND INDEED ! So no "faaltu" baatein, help ! :p

Answer 8

Sorry, I don't do baby sitting :P

Answer 9

Now from where on this earth "baby sitting" came ? Iam asking you to help me solve an ECO(H) , 2nd year maths question , not to sing a lullaby ! :p Had hai matlab ! ;p

Answer 10

Thanks for honouring me with your MEDAL ! :P

Answer 11

Anyways I gtg now , hope to see the answer posted ! :p Cya ! :-)

Answer 12

You should not worr y about the denominator. It is continious at any x except at x=0.
All you have to examine is the function g(x) = [x].
Where is the function g(x) discontinuous?

Answer 13

See for example
http://mathworld.wolfram.com/IntegerPart.html

Answer 14

check right and left limits at x=-1/2 and x=1 If right limits are equal to left limits the function is continuous

Answer 15

Iam not able to deal with [x] ! :-(
When there is a positive number inside [x] , that's ok with me , but when there is a negative number , Iam not able to apply the left/right hand limit ! Please help

Answer 16

[-1.5] = -2.

More formally, \[ \lfloor-a \rfloor = - \lceil a \rceil \]

Answer 17

You do not have negative numbers now, you have 1 and 1/2

Answer 18

its -1/2

Answer 19

Ok apply LHL to [x] where x->-1/2

Answer 20

I did not see the -. I need better glasses.

Answer 21

[ -1/2 ] = [-0.5]=-1

Answer 22

[x} is constant at any open interval having end points n, n+1 or n is a positive or negative integer.

Answer 23

so -1/2 is in the interval (-1,0).
Is {x] continuous at -1/2?

Answer 24

Heya ! Iam finally through with this question. So before closing this question , I would like to thank all of you-" THANK YOU !" :-)