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Find the equation to the tangent to the curve x=cos(2y+pi) at (0, pi/4)

Normally to find a tangent we want to work out dy/dx, but since this equation is x=something, it's much easier to work out dx/dy first, then we get dy/dx by doing 1/(dx/dy)=dy/dx. By the chain rule, dx/dy = ...
SJ
Answered by Sarah J. • Maths tutor
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Find the angle between two lines with vector equations r1 = (2i+j+k)+t(3i-5j-k) and r2 = (7i+4j+k)+s(2i+j-9k)

Explain the dot product and the relation : a.b= ¦a¦ ¦b¦ cos(x) where a.b is the dot product of two vectors, ¦a¦ and ¦b¦ are the magnitude of a and b respectively and x is the angle between them. Since the an...
MS
Answered by Muhammad S. • Maths tutor
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Find the intersection coordinates of both axis with the function: f(x)=x^2-3x+4/3

Find the y 1 coordinate, where x 1 = 0, this is the intersection with y-axis. f(0)=4/3, therefore one intersection P y =[0,4/3]Find the x 1,2 coordinates, where y = 0, this are the intersections with x-axis....
MS
Answered by Martin S. • Maths tutor
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Integrate the natural logarithm of x (ln x) with respect to x

In order to integrate ln x you have to use integration by parts, even though it appears there is only one term to be integrated. We get around this by instead writing it as (ln x)(1), where we treat the 1 as...
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Answered by Archie D. • Maths tutor
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a) Express 4(cosec^2(2x)) - (cosec^2(x)) in terms of sin(x) and cos (x) and hence b) show that 4(cosec^2(2x)) - (cosec^2(x)) = sec^2(x)

A) 4(cosec 2 (2x)) - (cosec 2 (x)) = 4/(sin 2 (2x)) - 1/(sin 2 (x)) = 4/[(2 sin(x) cos(x)) 2 ] - 1/(sin 2 (x)) B) 4/[(2 sin(x) cos(x)) 2 ] - 1/(sin 2 (x)) = 4/(4 sin 2 (x) cos 2 (x)) - 1/(sin 2 (x)) = 1/(sin...
MR
Answered by Mario R. • Maths tutor
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