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HSC 2015 MX2 Marathon (archive) (1 Viewer)

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Sy123

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Re: HSC 2015 4U Marathon

An easier question:

 

Sy123

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Re: HSC 2015 4U Marathon

I tried doing that but i get :

Am i doing something wrong?
Rather use
Intuition behind this transformation is that we want an inequality with an ln() function in it because the RHS has a ln() function
 

Kaido

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Re: HSC 2015 4U Marathon

Show that it's greater than the sigma notation taylor series for e^x?
 

Ekman

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Re: HSC 2015 4U Marathon

Rather use
Intuition behind this transformation is that we want an inequality with an ln() function in it because the RHS has a ln() function
After that all I did was:



And you sum both sides to get:



Which gets you to the final inequality.

Edit: Nvm Sy did it above
 

InteGrand

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Re: HSC 2015 4U Marathon

With these inequalities, if you can't see how to do it, it may help to start from the statement you want to prove and use biconditional steps (basically if and only if steps) to simplify it:



and this latest equivalent inequality may be easier for you to prove using part (i).
 

Ekman

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Re: HSC 2015 4U Marathon

Yes, or a more intuitive way of looking at it:









It should be a HSC standard question
Just out of curiosity, when making the substitution x=1/k, would we need to state conditions for k in order for the inequality to exist? For example, in this question, would we need to state
 

Sy123

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Re: HSC 2015 4U Marathon

Just out of curiosity, when making the substitution x=1/k, would we need to state conditions for k in order for the inequality to exist? For example, in this question, would we need to state
Better safe than sorry
 

InteGrand

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Re: HSC 2015 4U Marathon

Just out of curiosity, when making the substitution x=1/k, would we need to state conditions for k in order for the inequality to exist? For example, in this question, would we need to state
 
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