So I was away from my intro calc course for three classes because of tonsilitis ( Read more... )

Does anyone know of a good online pre-calc tutor ( Read more... )

So my teacher thought it would fun to go through a whole chapter on integrals while i was down with bronchitis.  uhh.. could someone help me with these problems ( Read more... )

Gandalf the Grey started in the Forest of Mirkwood at a point with coordinates (1, 2) and arrived in the Iron Hills at the point with coordinates (2, 6). If he began walking in the direction of the vector v=3i+2j and changes direction only once, when he turns at a right angle, what are the coordinates of the point where he makes the turn ( Read more... )

I recently got this problem wrong on a test, and it involves volume of a solid of rotation. For some reason I got stuck and tried to use arc length (since that was also being tested), but could someone please explain it to me?

( Problem + my work )

does this seem correct? i haven't had calc in a while and mathematica can sometimes do odd things.

( Read more... )

We're currently studying L'Hopital's Rule for limits in Calculus BC, particularly in application to logs. I just have a few questions:

( Limits fun )

ok, so i have a fairly simple integration by parts problem here but i am missing something.

it is integrate sec^2xtanxdx

i set it to be secx(secxtanx) and then i made u=secx du=secxtanxdx dv=secx(secxtanx)dx

so, then i got

integrate(secx(secxtanx)dx) = secxsecx - integrate(secx(secxtanx)dx)

and i am back where i started. what i am missing?

I'm sorry if this question may seem elementary:

Calculate the integral of (x^3)(e^-(x^(2)))dx

I solved it as follows:
---
u=x^2
du=2xdx

(1/2) Integral ue^-(u)du = (-1/2)(u^2/2)(e^-u) + C = (-1/4)(x^4)(e^-(x^(2))) + C.
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Online integrators tell me that the answer is (-1/2)e^-(x^(2))(x^2 + 1).

What am I doing wrong?

I'm in a basic sets and logic course, and we're working through induction. I'm supposed to prove: (∀n ∈ N)(Σ r.r! = (n+1)! - 1), where the lower bound is r=1, and the upper is n, and N is the natural numbers. The only thing is that I have no idea how r.r! works. Any help I'd appreciate.