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Let P(n) be the statement “(n^3)-n is divisible by 3”

First we’ll examine the base case: P(1)

(n^3)-n=1^3-1=1-1=0

0=3*0, so is divisible by 3, and so P(1) is true

Now assume fo...

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f'(x)=( sqrt (x^2+1) - x * ( x / sqrt (x^2 +1) ) ) / (x^2+1) = (x^2 + 1 + x^2) / ( (x^2 + 1) * sqrt ( x^2 + 1) ) =  1 / ( (x^2 + 1) * sqrt (x^2 + 1) ). 

f'(x) > 0 for any x => f is increasing...

Traditionally, the focus of state-hood was state-centric, states were expected to exercise full jurisdiction internally and depend on self-help; states were independent on the world stage. Similarly, the ...