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Given that dx/dt = (1+2x)*4e^(-2t) and x = 1/2 when t = 0, show that ln[2/(1+2x)] = 8[1 - e^(-2t)]

1/(1+2x) dx = 4e^(-2t) dt Integrate both sides: ln[2/(1+2x)] = -8e^(-2t) + c input x = 1/2, t = 0: ln(2/2) = -8*(1) + c ln 1 = 0, so c = 8ln[2/1+2x] = 8[1-e^(-2t)]
HF
Answered by Henry F. • Maths tutor
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Solve: 2 sin(2x) = (1-sin(x))cos(x) for 0<x<2*Pi and give any values of x, if any, where the equation is not valid

Double angle formula:Sin(2x) = 2sin(x)*cos(x)==&gt; 2sin(x)*cos(x) = (1-sin(x))*cos(x) (2sin(x)-1+sin(x))*cos(x) = 0(3sin(x) - 1)*cos(x) = 0 i) cos(x) = 0, ii) 3sin(x) = 1 ==&gt; sin(x) = 1/3 i) x = Pi/2, 3P...
HF
Answered by Henry F. • Maths tutor
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How do I find the maxima and minima of f(x) = e^(x^2)?

When dealing with maxima and minima points, there are two ways to go, one of these is to first compute the first derivative of the function, check when this function is zero, and then study its sign; the oth...
JA
Answered by Jacob A. • Maths tutor
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Q4 on 2017 Edexcel C4 paper, concerns differentiation of multiple variables.

(a) Asks to differentiate an equation C: 4x 2 - y 3 - 4xy + 2 y = 0Then use the fact that point P (-2,4), lies on C to find an expression for dy/dx Differential of form 8x - 3y 2 (dy/dx) - (4y + 4x(dy/dx)) +...
AW
Answered by Alexander W. • Maths tutor
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The complex numbers Z and W are given by Z=3+3i and W=6-i. Giving your answers in the form of x+yi and showing how you clearly obtain them, find: i) 3Z-4W ii) Z*/W

i) 3Z-4WFor this question it is just the matter of substituting the complex numbers of Z and W into the equation. So, 3(4+3i)-4(6-i). Then multiply out the brackets to get 12+9i-24+4i. Finally simply to get ...
JB
Answered by James B. • Maths tutor
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