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Express 1/(1+2x)(1-x) in partial fractions

1/(1+2x)(1-x)=(A/(1+2x))+(B/(1-x))1=A(1-x)+B(1+2x) Now set the bracket of one of A or B equal to 0 to get an equation with 1 unknown.Set x=11=A(1-1)+B(1+2(1))1=A(0)+B(3)1=3BB=1/3Set x=-(1/2)1=A(1-(-1/2))+B(1...
LC
Answered by Luke C. • Maths tutor
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How do you find a turning point of a function using differentiation?

To find the location of turning points on a function, find the first derivative of the function, and then set the result to 0. if you then solve this equation, you will find the locations of the turning poin...
NS
Answered by Nathan S. • Maths tutor
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A particle A of mass 0.1kg is moving at a speed of 1.5m/s to the right. It collides with a particle B of mass 0.3kg moving at a speed of 1.1m/s to the right. Calculate change in momentum of particle A if particle B has a speed of 1.4m/s after collision.

Momentum is conserved during the collision.Momentum = mass x velocityMomentum before = momentum after(mv) P1 + (mv) Q1 = (mv) P2 + (mv) Q2 (0.1 x 1.5) + (0.3 x 1.1) = 0.1v P2 + (0.3 x 1.4)v P2 = 0.6m/sChange...
JS
Answered by Juliet S. • Maths tutor
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What is the area under the graph of (x^2)*sin(x) between 0 and pi

To solve this integral you need to use integration by parts twice. You separate the two term in the integral into x^2 and sin(x). You then multiple x^2 by the integral of sin(x) (-cos(x)) and apply the upper...
KP
Answered by Khalil P. • Maths tutor
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A curve has parametric equations x = 1- cos(t), y = sin(t)sin(2t). Find dy/dx.

Here we have x(t) and y(t) which are both functions of t, but we want dy/dx, which doesn't involve t, we therefore need to use the chain rule. The chain rule tells us that: dy/dx = (dy/dt) x (dt/dx).y = sin(...
WM
Answered by William M. • Maths tutor
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