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lets try a few integrations. what is integral of dx/(1+x)? You can see that it is in the form of f'(x)/f(x) so it is ln[f(x)] right? now what about integral of (e^x/(1+e^x))dx that is also in the form of ...

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...

With questions about projectiles, such as a ball travelling in the shape of a parabola through the air as in the above question, it is always good to split the problem into the horizontal and vertical com...

Shakespeare illustrates that at the beginning of the play, Lear’s views on how family love is expressed and measured is corrupt as his two insincere daughters are rewarded while his most loving and most l...

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...