Calculus project

[shelaby]

Quick i need a calculus project for tomorrow.

like a poster of some cool calc problem or maybe some 3d objects or sumthin.

If any calc wizards have any cool problems or anything cool to do with calc let me know

thanks guys

-Brendan

 

[duragezic]

You could beat the .9r = 1 some more.

 

[shelaby]

....

 

[DrPizza]

I dunno...
I found the following limit to be somewhat non-intuitive for the average calculus student. A proof of why may be interesting.

Lim (x -> 0+) Sqrt(x + sqrt(x + sqrt(x + sqrt(x + ...

= 1
(a lot of people think it would approach 0)

To prove, let L = sqrt(x + ...
add x to both sides
take the sqrt of both sides
sqrt(L + x) = same right side.
so, sqrt(L + x) = L
square both sides,
solve for L
take the limit as x->0 from the right

 

[eLiu]

Integrate exp(-x^2/2) from -infinity to +infinity

 

[thetman]

got any others? im in the same class as him and i need one too

 

[Cawchy87]

http://online.redwoods.cc.ca.us/instruc...nold/CalcProj/Fall97/erane/astroid.htm

google my friend. learn it. love it.

 

[MAME]

integrate this: f(x) = do your own damn work more than a day before it's due

 

[SilentZero]

Originally posted by: MAME
integrate this: f(x) = do your own damn more than a day before it's due

WINNAR!

 

[PowerMacG5]

Proof of why e^(i*Pi)+1=0

 

[everman]

Do the limit as X->0 where X= Time left until it's due and how that relates to postcount.

 

[eLiu]

do some demos on the convergence of like...the bisection method vs secant method vs newton's method

if you're skilled, derive the convergence rates for those 3...this is kind of hard, so if you dont' get it, just make some graphs

edit: or talk about when the above mentioned methods can be made to fail/converge very poorly



edit2: or look up something called the "Romberg Method" and demonstrate how it can be used to speed up the trapezoid rule (integration), & when/why romberg will fail.


edit3: show why you CANNOT simply continue to decrease h when you do numerical derivatives to increase accuracy