Hi everyone.(adsbygoogle = window.adsbygoogle || []).push({});

I am having a problem trying to understand the solutions of a homework problem that I had. Really need some help!

Basically, I am trying to establish an inequality on kT using a given set of inequalities to work with.

we have

[itex]L \leq Q \leq H[/itex]

[itex]L \leq Q < Q+R_{1} \leq H[/itex]

and

[itex]L \leq Q < Q+R \leq H[/itex]

where [itex]R_{1} = -ln(kT+e^{-Q}) [/itex]and [itex]R = -ln[ \frac{kT}{1-e^{-Q}} ] [/itex]

we want to establish [itex]kT = e^{-L} - e^{-H}[/itex] by using some sort of sandwich from two inequalities.

However, there's this part of the proof that I could not comprehend:

We are able to reach [itex]L \leq H-L \leq H[/itex] and since [itex]L \leq Q \leq H[/itex], we set [itex]Q = H-L[/itex] into the inequality [itex]-ln[ \frac{kT}{1-e^{-Q}} ]+Q \leq H[/itex], and we can get [itex]kT \leq e^{-L} - e^{-H}[/itex]

This is the part I do not comprehend and there appears to be such techniques used a couple of times in other math courses I had taken before.

My understanding is that this is actually incorrect; we should build some bounds and try to achieve the inequalities.

Can anybody help me out here? I really apologise for not using LaTeX to type this out, as I have no clue with LaTeX myself. Will try to edit the parts if possible.

I have attached the homework's solutions up, it's Q7 iii in concern. There's some errors to it I personally feel.

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# Question on Inequalities

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