Recent content by nickalh

Congratulations on finding a much simpler solution, than I did. Your equation with arctan is nearly identical to the one I simplified everything into. The origin is at the point where x & b touch each other, I misread it the first time, for Hariraumurthy's answer. In hindsight, discovered...

Two things for *indefinite integrals*, always remember the constant of integration. Get all the easy points on quizzes & tests. Second, they only differ by a constant, right? So pick different constants of integration to compensate. +4 for one & +5 for the other. Very commonly when doing...

Isn't that assuming the optimal triangle is isosceles? From how I read the problem, the goal is to prove what you're assuming.

I knew some 4th degree function had the desired behavior. I just played around with wolframAlpha.com until I had the right graph. An even function is symmetric on both sides of the y axis. So only x^2 & x^4, & constant terms. I first tried x^4 +x^2 with various coefficients but that did...

Hints: Write out which letters are constants. Write out which letters are variables. I don't use either side connecting with the top vertex. This implies I'm not using Pythagorean theorem either. My version is based on Calculus I methods, with an esoteric derivative thrown in. Originally, I...

My main point: The word easy should not be in a tutor's vocabulary. Although, for those who have spent hours (sometimes hundreds) mastering various Calculus material, few if any of us thought it was easy to learn. The most effective method, for most students is to realize, not only u=x+1...

Borhok has the right method again. Shemer77, would you let us know if you've gotten the right answer from Bohrok's information or still have further questions? Thanks.

Does this exercise allow us our own equations? Why not simplify it with? "y= x^2/2+30,y=1/8 x^4 -x^2 +5" This allows us one integral with shell method.If that's not allowed, we'll need at least two separate integrations. Are you required disc/ washer method? I think this exercise is easier with...

I've got a system of 4 equations with 5 variables. It sounds worse than it is, because none of the 5 are particularly difficult, compared to http://www.mathematics2.com/Calculus/RegiomontanusAngleMaximizationProblem". That can simplify into one equation with two variables. Be sure to keep the...

I'm betting Bohrok is right. I always thought it was odd, but nearly every initial value problem I see specifies, y' and y. Rarely or ever, two points, y(a)=c, y(b)=d. Minor clarification: Should it be 0<= x <= 2\prod? Technically, as given it's an invalid problem.

This post edited to correct my mistake in this post: On first thought, although it's true for the basis. On second thought, it's still likely to lead us astray. See my earlier reply about the maximum. Some ideas for the inductive step would be: i. Let A= {2^k nonnegative numbers} & B=...

Duhhh, of course, my mistake.Fancy Notation: On my web browser, as part of the editing box, there's a sigma/sum/ ∑ sign at the right end of the row with, Bold, Italic, underline. Click it to open a whole slew of notations. This box considers ∑ an operator. There's also subscript and superscript...

Whoops, I switched the cardinalities of A & B. I have rewritten my previous post to be consistent with the rest of the thread. At first I was tempted to use 3 choose 2, but the right formula is even simpler. If necessary, write out the various possible functions from A to B. For simplicity...

Is this a theorem you've used in class? Get in the habit of justifying every statement at least knowing a reason in your mind. Ironically, even if the numbers we choose are maximized, there may exist other sets of k numbers which are not equal to the average, but (arithmetic mean)<= (geometric...

1=1 1-1 =0 1-1+1 =1 1-1+1-1=0 1-1+1-1+1=1 ... Does that series appear to be converging to zero or going to zero? I'm assuming by take it out to oo, you mean count up all the terms, and not what is the sum. Are there a countable number of terms or uncountable number of terms? In this...