Why is my proof wrong? (analysis)

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SUMMARY

The discussion centers around a mathematical proof involving the upper and lower Darboux sums for the function sin(1/x). The user incorrectly calculated the lower Darboux sum as -12 instead of the correct value of -2. The upper Darboux sum was correctly calculated as 2. The discrepancy in the sums leads to confusion regarding the proof's validity, particularly in relation to the epsilon value, which remains undefined in the context of the proof.

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I was trying to prove this, but something went wrong and I'm not sure what...

We know that the greatest value of sin(1/x) can be 1 and the lowest value can be -1...

We know that the upper darboux sum is...

[tex]U(f,P) = sup(f[t_{k-1} , t_t]) (t_k - t_{k-1}) = (1) (1-(-1)) = 2[/tex]


We also know that the lower darboux sum is...

[tex]L(f,P) = inf(f[t_{k-1} , t_t]) (t_k - t_{k-1}) = (-1) (1-(-1)) = -12[/tex]

So we know that...

[tex]U(f,P) - L(f,P) = 2 - (-2) = 4 > \epsilon[/tex]

Can anybody tell me where I went wrong?

Thanks in advance
 
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What are you trying to prove in the first place??

And don't there need to be summations in the [itex]U(f,P)[/itex] and [itex]L(f,P)[/itex]?? How did you choose P anyway?

I also don't see where -12 comes from. Did you mean -2?

What is [itex]\epsilon[/itex] supposed to be?
 

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