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y = artanh(x/sqrt(1+x^2)) , find dy/dx

Some of these examiners quite like asking students to find the derivative of an inverse trig or hyperbolic function to try and catch someone off guard. The best way to approach these is to first multiply ...

Answered by Eugene L. • Further Mathematics tutor

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Show that the sum from 1 to n of 1/(2n+1)(2n-1) is equal to n/(2n+1) by Induction

First we check that this is true for n=1: S₁ = 1/(1x3) which is equal to n/(2n+1) for n=1 therefore S_n= n/(2n+1) is true for n = 1. Next assume that it is true for n=k. S_k

Answered by Jamie F. • Further Mathematics tutor

12933 Views

Two planes have eqns r.(3i – 4j + 2k) = 5 and r = λ (2i + j + 5k) + μ(i – j – 2k), where λ and μ are scalar parameters. Find the acute angle between the planes, giving your answer to the nearest degree.

Summary of solution: To find the angle between the planes, we must find the normal vector to each plane and then use the scalar product to find the angle between these two normal vectors....

Answered by Daniel C. • Further Mathematics tutor

6992 Views

Find the four complex roots of the equation z^4 = 8(3^0.5+i) in the form z = re^(i*theta)

We know that z=re^(itheta) from the definition of the exponential form of a complex number. Hence it follows that: z^4=(re^(itheta))^4=r^4e^(4itheta) We can find z^4 by converting 8(...

Answered by George G. • Further Mathematics tutor

5391 Views

Find, without using a calculator, integral of 1/sqrt(15+2x-x^2) dx, between 3 and 5, giving your answer as a multiple of pi
To get the denominator into something usable, you have to complete the square so you have it in one of the forms you can use a trig or hyperbolic substitution for. The minus sign in front of the x2 means ...
Answered by Luke D. • Further Mathematics tutor
3944 Views

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y = artanh(x/sqrt(1+x^2)) , find dy/dx

Show that the sum from 1 to n of 1/(2n+1)(2n-1) is equal to n/(2n+1) by Induction

Two planes have eqns r.(3i – 4j + 2k) = 5 and r = λ (2i + j + 5k) + μ(i – j – 2k), where λ and μ are scalar parameters. Find the acute angle between the planes, giving your answer to the nearest degree.

Find the four complex roots of the equation z^4 = 8(3^0.5+i) in the form z = re^(i*theta)

Find, without using a calculator, integral of 1/sqrt(15+2x-x^2) dx, between 3 and 5, giving your answer as a multiple of pi

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