Integrals of the exponential function

magnifik
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What is the problem? You are told exactly what to do so do it! You are told that e^x\ge 1 for all x\ge 0 so
\int_0^x e^t dt\ge \int_0^x dt
What does that give?
 

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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