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wunderkind
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Prove to me mathematically that if I start walking form one end of a room that I will eventually reach the other side. Be sure to include formulas!
(hint: use calculus)
(hint: use calculus)
Originally posted by Vodka
i did this one before, i'll try to see if i can find it... all i remember is that it has to do with limits [duh] because a finite distance when broken into an infine number of parts is still finite when added back together.
Originally posted by DeadWolfe
I *think* that depends on your views regarding the axiom of choice.
Ever heard of the Banach-Tarski paradox?
Originally posted by selfAdjoint
Heh! That deserves a thread all to itself!
.Originally posted by modmans2ndcoming
heh...I guess this is what you expected in a board full of Physics enthusiasts and artists (aparently they like hanging out here)
anyway, it goes somehthing like this
the Limit as x -> infinity of the nth term function of the series:
1/2 + 1/4 + 1/8 + 1/16...
you will find that the limit of this is 1, so you will reach the other side of the room.
Allah said:Quantum mechanics tells us that there are parallel universes. Therefore in a parallel universe, you have already reached the wall.
DeadWolfe said:.
Any particular reason you chose that equation?
Chaos' lil bro Order said:Since you said its a room it must have a finite length other wise it would not be a room. Therefore any motion forward (walking) even if its at an extremely acute angle like 1 degree orthogonal to the wall at your back, means that you are imparting some velocity forward towards the wall that's your destination.
You may argue that the room is infinitely long, but then I would answer it is not a room, but a hallway with one wall at your back.
Forget the math.
Calculus is a branch of mathematics that deals with the study of rates of change and accumulation. It is divided into two main branches: differential calculus, which deals with the study of rates of change, and integral calculus, which deals with the study of accumulation.
A calculus problem can be considered interesting if it requires the application of various concepts and techniques in calculus, and if it challenges the problem solver to think critically and creatively.
Some common techniques used to solve interesting calculus problems include taking derivatives, finding antiderivatives, using the fundamental theorem of calculus, and applying various integration techniques such as substitution, integration by parts, and partial fractions.
The best way to improve your skills in solving interesting calculus problems is to practice regularly. Start with simpler problems and gradually work your way up to more complex ones. It is also helpful to review and understand the underlying concepts and techniques used in calculus.
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