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Further Mathematics
A Level

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...

Answered by Douglas H. Further Mathematics tutor
2149 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)...

Answered by Tutor294323 D. Further Mathematics tutor
3209 Views

Find the derivative of the arctangent of x function

y = arctan(x)Start by taking the tangent of both sides:tan(y) = xTake the derivative of each side with respect to x, using implicit differentiation/the chain rule for the LHS, then rearrange to make dy/dx...

Answered by Mitchell B. Further Mathematics tutor
1785 Views

MEI (OCR) M4 June 2006 Q3

The question may be seen here: https://pmt.physicsandmathstutor.com/download/Maths/A-level/M4/Papers-OCR-MEI/Combined%20QP%20-%20M4%20OCR%20MEI.pdf
i) Let A = 4E-4 W, B=1E4 m/s^2 s.t. P = mA...

Answered by Oliver K. Further Mathematics tutor
1937 Views

(FP1) Given k = q + 3i and z = w^2 - 8w* - 18q^2 i, and if w is purely imaginary, show that there is only one possible non-zero value of z

k = q + 3i and z = k2 - 8k* - 18q2 i. Plug k into w to give: z = (q + 3i)2- 8*(q - 3i) - 18q2 i. k means the compliment of k which just means that the ...

Answered by Emma M. Further Mathematics tutor
2277 Views

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