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Find integers A and B, such that (5x +4)/((2-x)(1+3x)) = A/(2-x) + B/(1+3x)

Adding the fractions on the RHS of the equation in the usual way gives A/(2-x) + B/(1+3x) = (A(1+3X) +B(2-X))/((2-X)(1+3X)) = (5x +4)/((2-x)(1+3x)) This gives an expression for the original numerator in term...
LF
Answered by Lorne F. • Maths tutor
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Find the vertex coordinates of parabola y = 2x^2 - 4x + 1

In this exercise I have to find the coordinates of the vertex of the parabola. Given the general equation y= ax^2 + bx + c , the value of a is 2, the value of b is -4 and the value of c is 1. In order to com...
MB
Answered by Martina B. • Maths tutor
13993 Views

The curve y = 2x^3 - ax^2 + 8x + 2 passes through the point B where x=4. Given that B is a stationary point of the curve, find the value of the constant a.

As B is a stationary point, the value of dy/dx at this point must be equal to 0. Differentiating y gives this to be dy/dx = 6x 2 -2ax+8. At point B , x=4 . This gives the relation 104=8a and thus gives a=13.
EH
Answered by Evan H. • Maths tutor
9160 Views

How do you integrate x* (exp(x))??

The easiest method to use in this incidence is integratation by parts. So let u=x and dv/dx=exp(x). Therefore du/dx=1 and v=exp(x). Then we use the formula where integral(u du/dx)=u v-integral(v*du/dx). So i...
HJ
Answered by Harmony J. • Maths tutor
12049 Views

Differentiate y=x^3*(x^2+1)

As this is a product of two functions it is necessary to use the product rule for differentiation. Therefore one of the functions must labeled v and the other u. i.e. u=x^3 and v=(x^2+1). It is then necessar...
BJ
Answered by Bevan J. • Maths tutor
4150 Views