leehuan's All-Levels-Of-Maths SOS thread (1 Viewer)

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Paradoxica

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Okay, as it stands, I do not have the cartesian equation, even though I derived it from the parametric equation. This is strange.
 

seanieg89

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Okay, had another look at it after my meeting today. My parametric form looks correct, and leads to a cartesian equation pretty straightforwardly.



I am sure the analogous computations for the hyperbola are quite similar.
 

leehuan

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This is messing with my head thoroughly (+ I am tired of course).



Given answer (where I'm pretty sure the ^T is just transpose, because they love column vectors)

 

agha

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Some exercises in formal logic:









For a list of the symbols used see here
 
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leehuan

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A few questions this time:


---> Not too sure how to prove that the integral from 1 to xy is the same as from x to y



 
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leehuan

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You may NOT assume that the logarithm and the exponential functions are inverses AS exp: R -> [0, inf) is defined OUT of the inverse function theorem and is not proven in advance here.

I.e. I require the answer that STRICTLY uses the fundamental definition please
 

seanieg89

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For 2) it is just sin(1)/3 because k=3 is the first time its positive, and for k>3, the thing is bounded by 1/4 which is smaller than sin(1)/3.
 

Paradoxica

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Okay, had another look at it after my meeting today. My parametric form looks correct, and leads to a cartesian equation pretty straightforwardly.



I am sure the analogous computations for the hyperbola are quite similar.
What is the area bounded by the entire curve?
 

Paradoxica

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If a number is the root of a polynomial with algebraic co-efficients, is that number itself necessarily algebraic?
 
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