#Limits help
slate snowBOT
little hornet
for question 6
is that the only way to prove it
because i disproved it by saying LHL=5 and RHL=-1/3
therefore LHL != RHL and the limit does not exist
slate snowBOT
Limits help
magic jewel
for question 6
is that the only way to prove it
because i disproved it by sayi...
how did u come up with LHL = 5 and RHL = -1/3 ?
magic jewel
Kinda, did you just plug "random" numbers?
little hornet
No for the LHL I plugged in -3 and for the RHL I plugged in -1
magic jewel
No for the LHL I plugged in -3 and for the RHL I plugged in -1
yeah i got it, my point is that the proof is not about plugging in numbers that are outside of the critical -2 but your conclusion of what happens the more you approach -2 from both sides
i think if you demonstrate more examples like LHL -3 -2.5 -2.1 and so on and for RHL: -1, -1.5, -1.9
little hornet
For previous questions I used this method and it corespponed with the answer
magic jewel
my point is i could also plug in for LHL: -1000 and for RHL: 1000 but the question is are they saying something about the limit at -2?
little hornet
In the solution they used -1.999 and -2.001 do I have to use those bounds too
Because I can prove it without being that accurate
They didn’t ask to show how it behaves so I though I could get away with how I did it
magic jewel
In the solution they used -1.999 and -2.001 do I have to use those bounds too
That's intentional because these values are very near -2 and thus you can make a better conclusion of the limits.
Proving without accuracy can work sometimes but it's not very beneficial, because by your statement I can plug any numbers that are outside of -2
Like LHL: -1000 and RHL: 1000 (really extreme)
I mean LHL: x = -3 => you get 5 and RHL: x = -1 you get -1/3
That's a good starting point but elaborating further on what happens with another approach from both sides like
LHL: x = -2.5 and RHL: x = - 1.5 and then comparing the outputs from your previous approaches, then you can make a more firm statement regarding the limits on both sides
This was my point
Because u asked if "your way" to prove is also right but basically you did the same thing like them, by pluggin some near value and then make a statement how the limits are from both sides.
I mean, imagine you don't know how the functions looks like.
By making some approaches and comparing the outputs you can form a better understanding proof regarding limits
little hornet
oh i understand now