Last question - last part yeah, I thought the intuition you needed would be great for a marathon question (short and sweet).CSSA 2012 iirc?
I didn't read the rest but i can already tell your confused. Unsurprising since this question is definitely out of the scope of the hsc. (note that you said f'(a)=0, which is note true in general).This is my attempt:
Ah I see there, well you just posted the solution for Step 1, if I get rid of the strength of the assumption and loosen it up is it correct?I didn't read the rest but i can already tell your confused. Unsurprising since this question is definitely out of the scope of the hsc. (note that you said f'(a)=0, which is note true in general).
Here's a further hint:
EDIT: So I read the second step and the idea of adding and subtracting the same term was good and is a pretty standard technique in analysis. However, it still has some subtle errors. Firstly, while this is mostly a superficial error, in your assumption your said f is only k times differentiable, this condition is too strong and infact contradicts what your trying to prove. The assumption should be f is k times differentiable. Secondly, there is a more subtle error and I leave it as an exercise to find it. but note that as it stands, if your n=k+1 step was correct then this would imply that any function that is differentiable once would be differentiable to all orders. (While this is obviously wrong to me, I'm unsure if a HSC student would have run across a counter example since this tends to be true for most functions encountered at a hsc level.)
Missing a factor of k!. Perhaps I should have given the form of the polynomial in my question but anyway, I think you should be able to prove the result if you know what the poly is.Ah I see there, well you just posted the solution for Step 1, if I get rid of the strength of the assumption and loosen it up is it correct?
EDIT: And I am guessing that:
??
Google taylor polynomials.Ah I see there, well you just posted the solution for Step 1, if I get rid of the strength of the assumption and loosen it up is it correct?
EDIT: And I am guessing that:
??
Done it!
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Is latex broken or something?
Just the main points will do, and like a one sentence explanation between each 'major' line of working (i.e. skip the non important algebra)Done it!
But solution too horrendous to type out in LaTeX.
I haven't done it but iirc, this was a question in a Grammar paper a while ago and the easiest way to do it was to take logs of both sides and then differentiate implicitly.Just the main points will do, and like a one sentence explanation between each 'major' line of working (i.e. skip the non important algebra)
Basically using implicit differentiation.Just the main points will do, and like a one sentence explanation between each 'major' line of working (i.e. skip the non important algebra)
Can you guys please post some difficult integration and conics questions?
I haven't learnt conics yet but this was on the second page (and no one answered all of it yet)
Did you mean the length of the tangent cut off by the coordinate axes?
Note, replace the 1 with a. The image in the graph sets a=1
Yes, edited now.Did you mean the length of the tangent cut off by the coordinate axes?