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Further Mathematics

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if y = (e^x)^7 find dy/dx

To solve the the problem we need to recognize what type of differentiation technique we shall be employing

y = (e^x)⁷

the x unction which we are diferen...

Answered by George I. • Further Mathematics tutor

4539 Views

Convert the general complex number z=x+iy to modulus-argument form.

Modulus-argument form implies that we should express z in terms of its straight line distance from the origin and the angle this straight line would make with the x axis. This is expressed as z = r e

Answered by Ben H. • Further Mathematics tutor

12159 Views

The cubic equation 27(z^3) + k(z^2) + 4 = 0 has roots α, β and γ. In the case where β=γ, find the roots of the equation and determine the value of k

This question was worth 8 marks in a 2015 FP2 paper. The first part of this question is tricky, but once we have found the roots it will be easy to plug them in to get the value of k:

Whe...

Answered by Ross G. • Further Mathematics tutor

5677 Views

The set of midpoints of the parallel chords of an ellipse with gradient, constant 'm', lie on a straight line: find its equation; equation of ellipse: x^2 + 4y^2 = 4

// Allow me to make the question more explicit: we have a set of lines of equal gradients ‘m’. We need to find a line through which the midpoints of the intersections of these lines with the ellipse; a...

Answered by Drew P. • Further Mathematics tutor

4745 Views

Prove by induction that n^3+5n is divisible by 3 for every natural number.

Proof by induction has three core elements to it. To start with you must prove that the statement is true for the 'basic case'. For the most part this is 1, but some questions state it is higher.

Answered by Philip D. • Further Mathematics tutor

13719 Views