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How do I find infimum and suprrmum of set
S : { cosx + sinx | x - real number } without graph?
S : { cosx + sinx | x - real number } without graph?
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#2
(Original post by Infinity ∞)
How do I find infimum and suprrmum of set
S : { cosx + sinx | x - real number } without graph?
How do I find infimum and suprrmum of set
S : { cosx + sinx | x - real number } without graph?
For the function
cos(x)+sin(x)
it is relatively simple to find the maximum value, by a simple trig transformation into a single trig term like
r*sin(x+a)
Can you manage to do this?
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#3
Think about the least and greatest value of sinx and cosx. So what's the glb and lub?
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(Original post by mqb2766)
The infimum and supremum are basically the maximum/upperbound of the set. The least and max upperbounds.
For the function
cos(x)+sin(x)
it is relatively simple to find the maximum value, by a simple trig transformation into a single trig term like
r*sin(x+a)
Can you manage to do this?
The infimum and supremum are basically the maximum/upperbound of the set. The least and max upperbounds.
For the function
cos(x)+sin(x)
it is relatively simple to find the maximum value, by a simple trig transformation into a single trig term like
r*sin(x+a)
Can you manage to do this?
Since. -1≤sin(x+a)≤1
This implies -√2≤√2sin(x+a)≤√2
Are -√2 and √2 the infimum and supremum of this set? I think no.
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(Original post by NotNotBatman)
Think about the least and greatest value of sinx and cosx. So what's the glb and lub?
Think about the least and greatest value of sinx and cosx. So what's the glb and lub?
What if i add lub and glb of both?
Then -2 will be inf and 2 will be sup. But this is not right approach. This will be true for set { sinx + cosy| x,y - real no}.
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#6
(Original post by Infinity ∞)
I think the single term for this function will be √2sin(x + a).
Since. -1≤sin(x+a)≤1
This implies -√2≤√2sin(x+a)≤√2
Are -√2 and √2 the infimum and supremum of this set? I think no.
I think the single term for this function will be √2sin(x + a).
Since. -1≤sin(x+a)≤1
This implies -√2≤√2sin(x+a)≤√2
Are -√2 and √2 the infimum and supremum of this set? I think no.
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#7
(Original post by Infinity ∞)
Least value for sinx and cosx is -1 and greatest is 1.
What if i add lub and glb of both?
Then -2 will be inf and 2 will be sup. But this is not right approach. This will be true for set { sinx + cosy| x,y - real no}.
Least value for sinx and cosx is -1 and greatest is 1.
What if i add lub and glb of both?
Then -2 will be inf and 2 will be sup. But this is not right approach. This will be true for set { sinx + cosy| x,y - real no}.
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(Original post by mqb2766)
Why do you think no? Sounds ok to me.
Why do you think no? Sounds ok to me.
Is this the right answer?
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#9
(Original post by Infinity ∞)
Okay then supremum and infimum for this set are respectively √2 and -√2.
Is this the right answer?
Okay then supremum and infimum for this set are respectively √2 and -√2.
Is this the right answer?
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(Original post by NotNotBatman)
This is not the approach I meant, perhaps stick to the other way of thinking (harmonic form) because root 2 is correct . Sqrt(1^2+1^2) = sqrt(2)
This is not the approach I meant, perhaps stick to the other way of thinking (harmonic form) because root 2 is correct . Sqrt(1^2+1^2) = sqrt(2)
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#11
(Original post by Infinity ∞)
-√2 and √2 are glb and lub. Right?
-√2 and √2 are glb and lub. Right?
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#13
(Original post by Subhajit1134)
Suprimum-√2 and imf-(-√2)
Suprimum-√2 and imf-(-√2)
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