Here's a link to the proof:
I'm lost at the first sentence.
I thought Fermat had an answer to it though.
Can someone explain the Tau function to me?
If there are no characters on top of the sigma and pi, does that mean n goes to infinity? Are those sequences at all?
What does Tau: N arrow Z mean? Best I can figure it means the natural numbers map onto the integers and this is somehow related to the function's values.
Why is this notation necessary if there already existed a function that was the twenty-fourth root of this one?
So N is the domain of the function and Z is the co-domain. It's pretty common (and useful) notation.
Explaining proofs using the formal limit definition to a first year calc student is difficult.
Deltas and epsilons everywhere
That or delay the formal definition until analysis because if kids are just being taught to manipulate symbols and not understanding how something actually works, they're not really gaining anything. Particularly when it's something with few actual applications like the limit definition. In calc 1, we were shown how to prove something using it and told explicitly we didn't really need to understand it.
Hey guys, I'm starting Numerical Analysis and Probability Theory and Statistics next semester. Anything I should know before hand? Which one requires the most work? I was thinking of getting the books already now and bringing one during my vacation.
I know this thread is quite old but I would like to know if this is good. I never did matrix nor Jacobian before but I'm learning by myself and I decided to try on spherical coordinates.
i had a maths competition today with a few tough questions that I couldn't answer, and I thought you guys might be interested to see 'em
3. Find a function f(x) whose derivative is equal to its inverse.
5. The equilateral triangle ABC has a circumscribed circle. A line originating at A passes through the line BC at the point D and through the circle at the point Q. Show that 1/DQ = 1/CQ + 1/BQ.
there was another one i didn't get but it was lame
He just didn't do it right.
1/y=dy/dx => ydy=dx => y^2/2=x => y=sqrt(2x)
My FP2 exam is tomorrow. I assume you'd all find it trivial if you did it now, correct?
I'm thinking since we have: f'(x) = f^-1(x)
Could try go somewhere with: f(f'(x)) = 1
Or differentiate both sides w.r.t x:
f''(x) = 1/(f'(x))
Nevermind, I think its got something to do with the golden ratio, lets see if this works...
Okay think about this, differentiating something in form ax^n gives you anx^(n-1), inverting something in form ax^n gives you something in form (x/a)^(1/n) so for powers we have n-1=1/n, solving gives the golden ratio, then we just need to find a.
After calculating a I get:
f(x) = (2/1+rt5)^(2/(rt5 - 1))*x^((1+rt5)/2) I can't be fucked to check if it works.
How hard is Further Maths AS/A2 in general? I'm on track to self-study it because of a clusterfuck in my scheduling, and I was wondering if it was feasible for me to complete both in the span of a year.
To clarify a little further: further maths AS is piss easy, A2 is rock hard.
I'm probably only going to do the further maths as level.
got 81% in first year of physics. YAY!
Is the kth degree taylor series of a function guaranteed to be the best fit polynomial of degree k for that function?
Of course for any specific point on the curve (as opposed to best fit in a general region) you wanted to approximate, you could do better by simply using a line that passes through the curve at the point that you want to approximate, and the point on the curve where you're taking the Taylor series around.
I'm not sure exactly how to quantify how good a fit it is, possibly by finding the area between the approx and actual curve.
i have decided that statistics are the würst
I need to find a better way to phrase my question, I think.