#I need some clarification on if my workings are correct
queen oriole
icy spire
What's the problem Timi? Do you want to check it?
icy spire
Ok
primal plazaBOT
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icy spire
You have done this mistake in every problem
Let me tell you the right way to solve the inequality you wrote
primal plazaBOT
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icy spire
,w (2x+4)/(5x+2) < 1
primal plazaBOT
icy spire
So you gotta make this right
But the inequality we want is of absolut value
,w -1 < (2x+4)/(5x+2) < 1
primal plazaBOT
icy spire
@queen oriole see the answer
You made same mistake in all the exercise questions so yeah that need correction
Answer 6 seems wrong too. Exercise 2 seems fine
queen oriole
Let me tell you the right way to solve the inequality you wrote
I don’t understand why the solution to my inequality is wrong
queen oriole
I don’t understand why the solution to my inequality is wrong
Oh wait. Hold on😂I’m doing the right thing here right?
icy spire
Wait
queen oriole
Answer 6 seems wrong too. Exercise 2 seems fine
Answer 6 has two solutions. One in red and one in black. I believe the red one is the right one. Correct?
icy spire
The thing given in red is about sequence as far as I can see, for a series to be convergent it's sequence must be convergent to 0
But that's not a sufficient condition
primal plazaBOT
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icy spire
What's the answer to this according to you? @queen oriole
queen oriole
(-1,0) union (1,infinity)
But I don’t know why this is the answer. Our professor just told us
icy spire
But I don’t know why this is the answer. Our professor just told us
I'll tell you
Do you know the inequality sign changes when both sides are multiplied by negative numbers
primal plazaBOT
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primal plazaBOT
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queen oriole
Do you know the inequality sign changes when both sides are multiplied by negati...
Yeah
queen oriole
But this only holds for x>0
x>1 you mean?
icy spire
So we havetwo cases, $x>0 \land 1<x²$ and $x<0 \land 1>x²$
primal plazaBOT
fäf
icy spire
x>1 you mean?
No I mean x>0
queen oriole
x>1 you mean?
Wait. I meant, x would be > 1. Right?
queen oriole
We make two cases alright
alright
queen oriole
In first case x is negative and in second case x is positive
Where is this? Where are we?
icy spire
1/x < x gives us 1 > x²
When x is positive
1/x < x gives 1<x²
The inequality depends on the sign of x
Are you confused @queen oriole ?
queen oriole
I’m still a bit confused
queen oriole
Are you confused <@886168396490752001> ?
Yes
icy spire
Ok lets go with numbers
queen oriole
Alright
icy spire
1/-1 < 2 , if I multiply the -1 on both side, I'll get 1 > -2 right
Or will it stay 1 < -2
queen oriole
Or will it stay 1 < -2
No
icy spire
In same way if x is negative and you multiply it on both sides of 1/x < x , what would happen
x (1/x) > x (x) , right?
The sign will change
queen oriole
But why are we dealing with -x?
icy spire
Yes
queen oriole
Okay. I’m following
icy spire
If x is negative the sign of inequality will change when we multiply both sides with x
If x is positive the sign of inequality won't change when we multiply both sides with x
2 cases
We have to think about both
We don't have to consider x as some positive number and multiply like 1/x < x gives 1 <x² no
We have to make cases
If x is negative (x<0); 1/x<x imply 1>x
If x is positive (x>0); 1/x > x imply 1>x²
queen oriole
Like this?
icy spire
No no don't think like that
x takes negative values too right
x=-1,-2,-3 and all
We have to make cases for such values
queen oriole
x takes negative values too right
Which x would be negative?
icy spire
When x is negative meaning x takes values like -1 or -2 , in that case if we multiply x on both side the sign of inequality will change cuz it's negative
I gtg rn can help you later
queen oriole
queen oriole
I gtg rn can help you later
Alright. Thank you
fading oasisBOT
@queen oriole has given 1 rep to @icy spire
icy spire
Just think on this