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integrate by parts the equation dy/dx = (3x-4)(2x^2+5).

The equation we use to integrate by parts is y = uv - ∫ v(du/dx) dx + c so we separate dy/dx into u=(3x-4) and dv/dx=(2x 2 +5) however we still need to find du/dx and v, by differentiating u (bring the power...
AH
Answered by Abby H. • Maths tutor
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What is de Moivre's theorem?

de Moivre worked out a brilliant and beautiful way to solve complex equations. If you for example have z 3 = 1 and you want to find all real and complex z that satisfy this equation. i is just a complex numb...
FD
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solve for x: (x-2)(x+3)=2(2x+11)

expand the brackets to get x 2 -2x+3x-6=4x+22 bring all the terms to one side x 2 -2x+3x-6-4x-22=0 (remember:if you do something to one side, do the same thing to the other! e.g. -4x on both side) gather all...
JR
Answered by Jack R. • Maths tutor
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A curve is defined by the parametric equations x=t^2/2 +1 and y=4/t -1. Find the gradient of the curve at t=2 and an equation for the curve in terms of just x and y.

To find the gradient of the curve at t=2 we need to find an expression for dy/dx and then substitute in for t=2. We can make use of the chain rule to find this expression because dy/dx = (dy/dt)/(dx/dt) and ...
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Answered by Steven C. • Maths tutor
9331 Views

Solve the inequality. x^2 + 2x -15 > 0

To solve the inequality, it must first be factorised. This could be done by the ‘complete the square’ method. However in this example it is more efficient to find a pair of numbers that multiply to give the ...
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Answered by Elizabeth F. • Maths tutor
13629 Views