Math Is Fun Forum

Colin Qi

Guest

Limit proof

1) If g(x) = -x^5 -x^4 +x^2 +1, prove that there is a number c such that g(c) = 1.
Can't u just put in a zero and get 1? I don't know how to prove it tho?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Limit proof

That's a perfectly good proof for that question, but other questions might not be as nice.

In general, you should find a value a such that g(a)<1, and another value b such that g(b)>1.
Then, because g(x) is a polynomial and therefore continuous, there will be a value c between a and b that gives g(c)=1.

Last edited by mathsyperson (2007-09-17 05:23:41)

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Why did the vector cross the road?
It wanted to be normal.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Limit proof

mathsyperson meant:

find a value a such that g(a)>1, and another value b such that g(b)<1.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Limit proof

...Oops. Nice catch.

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Why did the vector cross the road?
It wanted to be normal.