Real analysis - differential/sequence

foxofdesert
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Homework Statement



I attached a .bmp file

Homework Equations





The Attempt at a Solution



I don't get this one at all. Since f is differentiable, the interval [a,b] must be continuous, and I cannot use rational/irrational tricks like in limit problems. does anyone have suggestions?
 

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should I just assume that x=c and xn -> c as n->inf?
 

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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