Valid HL Maths Proof?

arboroia

Would a new way of proving an equation be acceptable? (Don't know if it's new but is the below ok in the exam?)

Prove:


1.

2. Therefore using first principles:

3. Binomial:

4. Cancel first x^n with -x^n and then divide every term of binomial by h.

5. Left with

6. Wipe the h's using the limit and left with

Is that valid?

Patriciamc93

It would be correct yes however I am pretty sure for that proof they say prove by induction. That would mean you would have to do it by induction methods. But if they dont mention induction and just say prove....... Etc. Then your way would be right and you could argue that if they did not give you marks for it.

Gumbi

Generally the differential rule needs to be proven by specifally induction methods.

partyatmygaff

Did you write this yourself using the LATEX tags?

As for the actual proof itself, i'm not so sure. At step 5 where you have [LATEX]{n\choose n}(X^0)(h^n-1) [/LATEX] wouldn't that end up being -1 and not simply 0 when h tends to 0?

MathsManiac

Think that was a Latex typo. Should have read [LATEX]{n\choose n}(x^0)(h^{n-1}) [/LATEX].

The proof is valid, unless you're specifically asked to do it by induction, and it's worth noting the syllabus does say "Proof by induction that..."

arboroia

Yup I wrote it myself in latex - takes a quite a while to do, but is faster than explaining otherwise.

That's fine then, I always try to do prove the theorems by trying it myself first and if it doesn't work out, learn them off.

Thank you everyone!

edit: didn't know latex existed on boards.ie so I inserted some from another dynamically generating latex ebsite where I typed URL/?latex-code-here