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Probability can be highly intuitive yet at times completely nonsensical. Famous mathematicians have fallen victim to the idea that everything in probability can be done without rigorous calculation and th...

  The turning point of a curve can be visualised in your head (or on paper/screen using diagram) as the point in which the curve charges direction – and at this point the gradient of the curve is equal to...

v=ln2, x=2ln2 - 2

aim is to move all numbers to one side and all the x to one side.
whatever you do to one side, you must do to the other side.
For example I want to remove -9 on the left by adding +9 to left si...

A/(3+x) + B/(1-x) + C/(2x+1) = (9x^2 + 43x + 8)/(3+x)(1-x)(2x+1)So... A(1-x)(2x+1) + B(3+x)(2x+1) + C(3+x)(1-x) = (9x^2 + 43x + 8)Insert x=1Equation becomes 12B = 60 so B = 5.Then insert x=-3Equation beco...