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Further Mathematics
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Sketch the locus of z on an Argand diagram if arg[(z-5)/(z-3)] = π/6

Rewrite as arg(z-5) - arg(z-3) = π/6 and let arg(z-5) = b and arg(z-3) = a, so that b-a = π/6Since we know that each argument makes a half line (starting at (3,0) for angle a, (5,0) for angle b) the half ...

FA
5140 Views

Given f(x)= 8 − x^2, solve f(3x) = -28

First substitute (3x) into the equation for f(x), giving f(3x) = 8 - 9x2. This is then equal to -28 and so it is remains to solve the equation 8 - 9x2 = -28. This can be written as 9...

GG
3556 Views

solve the 1st order differential equation 2y+(x*dy/dx)=x^3

1st we note our three methods for solving 1st order differential equation: separating the x and y variables to both sides of the equation, and integrating both sides with respect to x. Recognising an exac...

DH
2420 Views

find the stationary point of the curve for the equation y=x^2 + 3x + 4

dy/dx = 2x +32x + 3 = 0x= 3/2(3/2)2 + 3(3/2) + 4 = 2.25 + 4.5 + 4 = 10.75

IH
2897 Views

Write the Maclaurin’s series for f(x)=sin(3x)+e^x up to the third order

 To simplify this question, it is possible to expand the two elements of the function and then add the two expansions together.First, the expansion of sin(3x) around the origin is sin(30)+d/dx sin(3x)...

TD
3595 Views

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