can someone tell me what’s the mistake I am making | Mathematics | Page 1

hexed lynx Dec 31, 2023, 8:59 AM

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can someone tell me what’s the mistake I am making?
QUESTION:
given x ∈ (-1,1)
In which interval does x-x^2 belong?
MY ANSWER:
x ∈(-1,1)
x^2 ∈(0,1)
-x^2 ∈(-1,0)
x-x^2 ∈(0,1)

ashen birchBOT Dec 31, 2023, 8:59 AM

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hexed lynx can someone tell me what’s the mistake I am making? **QUESTION**: given x ∈ (-1,...

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hexed lynx Dec 31, 2023, 9:00 AM

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can someone tell me what’s the mistake I am making

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can someone tell me what’s the mistake I am making?
QUESTION:
given x ∈ (-1,1)
In which interval does x-x^2 belong?
MY ANSWER:
x ∈(-1,1)
x^2 ∈(0,1)
-x^2 ∈(-1,0)
x-x^2 ∈(-2,1)

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Ping me please

tall sentinel Dec 31, 2023, 9:06 AM

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hexed lynx can someone tell me what’s the mistake I am making? **QUESTION**: given x ∈ (-1,...

Try analyzing the function in the given integral, specifically where it increases and decreases, its extrema (if there are any) and the one-sided limits at the borders of the interval.

hexed lynx Dec 31, 2023, 9:07 AM

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tall sentinel Try analyzing the function in the given integral, specifically where it increase...

So what I’m doing is wrong?

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I don’t understand why

tall sentinel Dec 31, 2023, 9:09 AM

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hexed lynx So what I’m doing is wrong?

It's not correct in general, as x increases while -x^2 decreases.

hexed lynx Dec 31, 2023, 9:09 AM

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But I have solved questions like this every time and I have gotten them correct

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Maybe numbers were involved

rocky sparrow Dec 31, 2023, 9:11 AM

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hexed lynx But I have solved questions like this every time and I have gotten them correct

people make mistakes all the time don't worry it happens sometimes

tall sentinel Dec 31, 2023, 9:11 AM

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hexed lynx But I have solved questions like this every time and I have gotten them correct

It's not like it never works, but this isn't a correct approach in general.

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Better to use the correct approach.

hexed lynx Dec 31, 2023, 9:12 AM

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But I’m actually confused what exactly is wrong in doing that sorry

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And can you help me do it the correct way

rocky sparrow Dec 31, 2023, 9:12 AM

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when dealing with such quadratics

hexed lynx Dec 31, 2023, 9:13 AM

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hexed lynx can someone tell me what’s the mistake I am making? **QUESTION**: given x ∈ (-1,...

I got one of the limit right whereas the other one is wrong

tall sentinel Dec 31, 2023, 9:13 AM

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hexed lynx And can you help me do it the correct way

I wrote above what you need to do.

rocky sparrow Dec 31, 2023, 9:16 AM

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,w graph x-x^2

deft haloBOT Dec 31, 2023, 9:16 AM

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rocky sparrow Dec 31, 2023, 9:16 AM

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see it's negative

hexed lynx Dec 31, 2023, 9:17 AM

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But I have a condition

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in the question

rocky sparrow Dec 31, 2023, 9:18 AM

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yes take -0.5

hexed lynx Dec 31, 2023, 9:19 AM

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I am getting this while applying my constraints

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Here it says that x-x^2 belongs to (-1,1)

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Very much different answer

rocky sparrow Dec 31, 2023, 9:20 AM

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ofc it's different

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range is

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positively additive

hexed lynx Dec 31, 2023, 9:20 AM

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I’m confused

tall sentinel Dec 31, 2023, 9:20 AM

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If x ∈ (-1, 1), then f(x) = x - x^2 ∈ (-2, 1/4].

hexed lynx Dec 31, 2023, 9:21 AM

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tall sentinel If x ∈ (-1, 1), then f(x) = x - x^2 ∈ (-2, 1/4].

Yes that is the answer but why does desmos give a different answer

rocky sparrow Dec 31, 2023, 9:21 AM

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-1 < x < 1 (1)
0 < x^2 < 1
-1 < -x^2 < 0 (2)
add 1 and 2
-2 < x-x^2 < 1

hexed lynx Dec 31, 2023, 9:22 AM

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That’s what I got

rocky sparrow Dec 31, 2023, 9:22 AM

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hexed lynx can someone tell me what’s the mistake I am making? **QUESTION**: given x ∈ (-1,...

-1+(-1) is not 0 it's -2

hexed lynx Dec 31, 2023, 9:22 AM

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Yes yes mb

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But that’s wrong too

tall sentinel Dec 31, 2023, 9:22 AM

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hexed lynx Yes that is the answer but why does desmos give a different answer

What do you mean?

hexed lynx Dec 31, 2023, 9:22 AM

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tall sentinel If x ∈ (-1, 1), then f(x) = x - x^2 ∈ (-2, 1/4].

This is the actual answer

rocky sparrow Dec 31, 2023, 9:22 AM

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that isn't wrong

hexed lynx Dec 31, 2023, 9:23 AM

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tall sentinel What do you mean?

I mean that I tried plotting the graph with my given conditions and this is what I get
According to this x is from -1 to 1

rocky sparrow Dec 31, 2023, 9:23 AM

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if you are talking about the smallest such interval

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just find the maximum via some calculus

hexed lynx Dec 31, 2023, 9:23 AM

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rocky sparrow -1 < x < 1 (1) 0 < x^2 < 1 -1 < -x^2 < 0 (2) add 1 and 2 -2 < x-x^2 < 1

I understand this but apparently this is wrong

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That’s what im saying

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It’s -2 <x-x^2< 1/4

rocky sparrow Dec 31, 2023, 9:24 AM

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brother this isn't wrong

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it might be insufficient

tall sentinel Dec 31, 2023, 9:24 AM

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hexed lynx I mean that I tried plotting the graph with my given conditions and this is what...

Yes, for -1 < x < 1 we get -2 < f(x) ≤ 1/4, which is visible from the graph.

hexed lynx Dec 31, 2023, 9:25 AM

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Oh yes

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But why is Teto saying -2 to 1

tall sentinel Dec 31, 2023, 9:27 AM

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I don't know.

hexed lynx Dec 31, 2023, 9:27 AM

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rocky sparrow -1 < x < 1 (1) 0 < x^2 < 1 -1 < -x^2 < 0 (2) add 1 and 2 -2 < x-x^2 < 1

This is incorrect right

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Lord

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Or is it correct

rocky sparrow Dec 31, 2023, 9:29 AM

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bro if it's between -2 and 1 it doesn't contradict it being in -2 and 1/4

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1/4 < 1

rocky sparrow Dec 31, 2023, 9:30 AM

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hexed lynx can someone tell me what’s the mistake I am making? **QUESTION**: given x ∈ (-1,...

try adding on, "smallest interval" maybe

tall sentinel Dec 31, 2023, 9:30 AM

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rocky sparrow bro if it's between -2 and 1 it doesn't contradict it being in -2 and 1/4

But we need the exact answer.

rocky sparrow Dec 31, 2023, 9:31 AM

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gilbert he didn't specify that at first

hexed lynx Dec 31, 2023, 9:31 AM

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Sorry my bad

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But yes we needed exact answer

rocky sparrow Dec 31, 2023, 9:31 AM

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oki

tall sentinel Dec 31, 2023, 9:32 AM

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hexed lynx But yes we needed exact answer

Try the approach I described above.

rocky sparrow Dec 31, 2023, 9:32 AM

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if we are talking about a general such function

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if we have minimum / maximum in the interval (a, b) then the derivative at that point is zero

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use this

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but sometimes the min/max is f(a) /f(b)

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so just in case check these values too

hexed lynx Dec 31, 2023, 9:35 AM

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Guys so I got the maxima

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But how to get the minima

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I got maxima as 1/4

rocky sparrow Dec 31, 2023, 9:36 AM

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hexed lynx But how to get the minima

as I said

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if the max/min is in (0,1)

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look at derivative zero

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and along with this check f(0)and f(1)

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these are the only max/min candidates

hexed lynx Dec 31, 2023, 9:37 AM

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Alright

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I got it

rocky sparrow Dec 31, 2023, 9:37 AM

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okk

hexed lynx Dec 31, 2023, 9:37 AM

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Thanks @rocky sparrow @tall sentinel

safe heartBOT Dec 31, 2023, 9:37 AM

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@hexed lynx has given 1 rep to @rocky sparrow @tall sentinel

tall sentinel Dec 31, 2023, 9:40 AM

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You're welcome!

rocky sparrow Dec 31, 2023, 9:46 AM

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Ill appreciate it if you give me something in return

hexed lynx Dec 31, 2023, 9:47 AM

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What do you want?

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I don’t have anything to give

rocky sparrow Dec 31, 2023, 10:12 AM

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hexed lynx I don’t have anything to give

refer the server to your friends

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help us in helping more people

hexed lynx Dec 31, 2023, 10:31 AM

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Sure

#can someone tell me what’s the mistake I am making