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gobbatron
New Member

USA
1 Posts

Posted - 10/16/2007 :  20:07:49  Show Profile
So my math teacher gave this to our high school class today.

I dont think he really expects any of us to get it, as its way beyond the course material we ahve been doing. Perhaps if someone here could solve it and explaint he math behind it i might be able to impress him? (and learn something on the way)

he gave us this:

let f be a function that satisfies the statement f(u+v)=f(u)+f(v)+1-cos(u*v) for all u,v
find f(0)

teacher says:come up with creative way of writing 0
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sahsjing
Advanced Member

USA
2399 Posts

Posted - 10/17/2007 :  16:13:20  Show Profile
As David said above, this one is really quite a simple one. Let u = v = 0, you can get the answer immediately.

Here is a similar problem I gave to my class:

Suppose f is a function that satisfies the equation
f(x+y) = f(x) + f(y) + xy + xy
for all real numbers of x and y. Suppose also that lim{x->0}f(x)/x = 1
Find f(0), f'(0), and f'(x).
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