Christos
  • Christos
calculus https://www.dropbox.com/s/md638a18l0e9v6g/Screenshot%202015-11-08%2012.07.56.png?dl=0
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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ganeshie8
  • ganeshie8
|dw:1446977489258:dw|
lochana
  • lochana
I think , 1 is the answer for all
Christos
  • Christos
and why is that

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More answers

ganeshie8
  • ganeshie8
1 is the answer for a, b, c
Christos
  • Christos
i would say c doesnt exist
Christos
  • Christos
because its not continues
lochana
  • lochana
@ganeshie8 What about d. isn't it 1 too?
ganeshie8
  • ganeshie8
what do you mean by "not continuous" ?
Christos
  • Christos
there is this little white dot that disconnects the wave
ganeshie8
  • ganeshie8
|dw:1446977616140:dw|
lochana
  • lochana
@Christos yes. That's right. I didn't notice that. a . 1 b. 1 c. doesn't exit d . doesn't exit
Christos
  • Christos
so its a)1 b)1 c)doesnt exist d)0
Christos
  • Christos
right ?
ganeshie8
  • ganeshie8
nope
Christos
  • Christos
why not
lochana
  • lochana
actually c is also 1.
ganeshie8
  • ganeshie8
The limit is about how the function behaves as you "approach the point" from either side. It doesn't matter if the function is continuous or not at that point. Even the function need not be defined at that particular point for the limit to exist.
lochana
  • lochana
let me explain. x--> +0 means you come along positive direction. x --> -0 means comes along negative direction x --> 0 means combination of both so c must be 1
Christos
  • Christos
@ganeshie8 is @lochana correct on this assumption ???
lochana
  • lochana
yes.
ganeshie8
  • ganeshie8
Yes |dw:1446977987755:dw|
Christos
  • Christos
oohh I see
ganeshie8
  • ganeshie8
since the function is approaching the same value from either side, we say the limit exists
Christos
  • Christos
ill give e medal to lochana so that you both have one :D
Christos
  • Christos
thanks a lot
Christos
  • Christos
to both
Astrophysics
  • Astrophysics
Just to clarify @lochana c does exist
lochana
  • lochana
@Astrophysics yes. After thinking sometime. I could understand that,.:)
Astrophysics
  • Astrophysics
Ah ok gotcha :) wanted to make sure
ganeshie8
  • ganeshie8
@Christos see if you can figure out if the limit exists as x goes to 3 in below graph of funciton : |dw:1446978247468:dw|
Christos
  • Christos
hmm
Christos
  • Christos
doesnt exists
Christos
  • Christos
i think
ganeshie8
  • ganeshie8
why ?
Christos
  • Christos
because the side limits are 1 and 4
Christos
  • Christos
so they are not equal
Christos
  • Christos
right ?
ganeshie8
  • ganeshie8
Perfect! As `x` approaches `3` from `left` side, the function is approaching \(\color{red}{1}\). As `x` approaches `3` from `right` side, the function is approaching \(\color{Red}{4}\). \(\color{Red}{1}\ne \color{red}{4}\) so the limit as `x` approaches `3` of the shown function `does not exist`.
Christos
  • Christos
:D
ganeshie8
  • ganeshie8
Just want to say this again and again. Notice that we are not bothered about whether the function is defined at `x=3` or not. As far as limit is concerned, all it matters is how the function behaves `around` x=3. We simply don't care whats going on exactly at `x=3`.

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