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MathEd-PII

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volunteer
I think we do not the sine and here is why I think that
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volunteer
we know that the vlaue is squeezed between -5x^2 and 5x^2 See what I mean?
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student
yes
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volunteer
and since the limits of those two without the sin are zero I *think* we can say that our limit is too.
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volunteer
Now we each need to look up the squeeze theorem.
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volunteer
It has soem other names too, but too maybe the pinch theorem
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volunteer
Here is a video maybe you can look at it later:
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volunteer
https://www.youtube.com/watch?v=some_math_video
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[ { "pii_type": "URL", "surrogate": "https://www.youtube.com/watch?v=some_math_video", "start": 0, "end": 47 } ]
student
thanks
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volunteer
I have *not* yet looked at it but I trsut https://www.khanacademy.org/math/calculus/limits-and-continuity/squeeze-theorem/v/squeeze-theorem-intro
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[ { "pii_type": "URL", "surrogate": "https://www.khanacademy.org/math/calculus/limits-and-continuity/squeeze-theorem/v/squeeze-theorem-intro", "start": 42, "end": 145 } ]
volunteer
should we try b now?
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student
yes
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volunteer
One commetn first
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volunteer
you see we know that the lim in a is between -5x^2 and 5x^2 because the min vlaue for sin -1 and the max is 1 OK?
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student
got it
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volunteer
OK I will ook at b now
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volunteer
IMO b is quite simialr
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volunteer
can u explain it?
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student
is it between -3 and 3
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volunteer
OK
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volunteer
I am looking in a book pls wait
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volunteer
I will type on the board oK?
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student
ok
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volunteer
see that so far?
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student
not really
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volunteer
does that help?
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student
yes
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volunteer
OK so for b, x -> 0
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volunteer
and can u tell what g(x) and h(x) are?
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student
3x amd cps 2/x
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volunteer
Student
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[ { "pii_type": "PERSON", "surrogate": "Student", "start": 0, "end": 7 } ]
volunteer
what does cps mean?
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student
*cos
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volunteer
I somewhat disagree
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volunteer
I think g(x) = -3x and h(x) = 3x
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volunteer
AND
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volunteer
f(x) x*cox(2/x)
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volunteer
does that help?
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volunteer
i mean f(x) =
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student
oh ok
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volunteer
3x*cos(2/x)
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volunteer
so we have -3x <= 3xcos(2/x) <= 3x
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volunteer
we know that because cos max is 1 and cos min is -1
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student
ok
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volunteer
and what is the lim x-> 0 of -3x ?
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student
am i substituting -3(0)cost (2/0)?
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volunteer
no u just sub 0 in 3x
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student
0
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volunteer
ok good and what abot lim x-> 0 of 3x ?
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student
0
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volunteer
good
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volunteer
so limx->0 3x*cos(2/x) is smadwiched between 0 and 0 !!!!
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volunteer
Good Yes
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volunteer
I see what you wrote
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volunteer
I will cricle in green and blue
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volunteer
The limit we want is squeezed between the green and blue limits See whagt I mean?
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student
so we just substite 0 for both expressions
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volunteer
yes the green and blue are quite simple functions and for *those* we can jsut sub
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volunteer
Student is not always true but it *is* true here
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[ { "pii_type": "PERSON", "surrogate": "Student", "start": 0, "end": 7 } ]
student
how to approach part c
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volunteer
OK I will read it pls wait
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volunteer
Interesting I am not sure but here is how I would start
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volunteer
sub x = 1 for g(x) = x^3 - 3x +4
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volunteer
and also in h(x) = -3x^2 +6x -1 OK?
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volunteer
OK that is good for the left (g(x))
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volunteer
ok so f(x) is squeezed (or sandwiche) between 2 and 2 !
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volunteer
and those 2 and 2 are the limits for g(x) and h(x) so what do u think?
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student
makes sense
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volunteer
so what is lim x -> 1 for f(x)?
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student
2
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volunteer
I agree
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volunteer
Now I am not sure why they give the interval you might chk with your tchr about that
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student
ok
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volunteer
Is this helping?
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student
yes
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volunteer
OK good please be aware that the squeeze theorem is sometimes called the pinch theorem and sometimes called the sandwich theorem
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student
ok
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volunteer
Do u have more?
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student
yes
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volunteer
OK first I will send another link
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volunteer
This one is good but be aware that Wikipedia oftenn gets highly technical after the first few paragrpahs
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volunteer
https://en.wikipedia.org/wiki/Squeeze_theorem
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[ { "pii_type": "URL", "surrogate": "https://en.wikipedia.org/wiki/Squeeze_theorem", "start": 0, "end": 45 } ]
volunteer
The do however, have some nice examples for this
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volunteer
especially "First example"
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volunteer
They say this too:
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volunteer
Also known as the pinching theorem, the sandwich rule, the police theorem
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volunteer
I never heard of the police theorem !!!
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student
is part b referencing squeeze theorem or is special limits another thing
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volunteer
part b from the previous group that we did?
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student
on the screenshot posted now it says Special limits using special limitzs
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volunteer
I do not yet see a new scrnshot
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volunteer
OK I had to scroll down
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volunteer
OK I think they want you to use the special limits given at the start of #2
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volunteer
Thos -- I htink -- are derived using the sq. theorem
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volunteer
But you need to use them as given
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volunteer
Can u do (a)?
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volunteer
I think what you wrote is undefined
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volunteer
0/0
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volunteer
I think you need to rewrite (a) using sin/cos
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volunteer
then we can proceed
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