Can Continuity at 0 Guarantee Equality at 0?

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Homework Statement



True or false? If f and g are continuous at 0 and f(1/(2n+7))=g(1/(7-2n)) for all positive integers n, then f(0)=g(0).

Homework Equations



lim x->0 f(x)=f(0)
lim x->0 g(x)=g(0)

The Attempt at a Solution



NO CLUE. My intuition says false.
 
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hi mathmajor2013! :smile:

hint: forget lim x->0 …

what is lim n->0 ? :wink:​
 
I'm wondering if tiny-tim didn't mean "n\to \infty"?
 
oops! :rolleyes:
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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