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Integral of ln x

xln(x) - x
OG
3196 Views

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 bot...
EL
7887 Views

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: S 1 = 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 = k/(2k+1). Now using this assu...
JF
15822 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. Breaking this down ...
DC
8679 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^(i theta) from the definition of the exponential form of a complex number. Hence it follows that: z^4=(re^(i theta))^4=r^4 e^(4 i theta) We can find z^4 by converting 8(3^0.5+i) (cartesian ...
GG
6709 Views