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Show that cosh(x+y) = cosh(x)cosh(y) + sinh(x)sinh(y)

RHS: cosh(x)cosh(y) + sinh(x)sinh(y) = 1/4(e^x + e^-x)(e^y + e^-y) + 1/4(e^x - e^-x)(e^y - e^-y) = 1/4(e^x.e^y + e^x.e^-y + e^-x.e^y + e^-x.e^-y + e^x.e^y - e^x.e^-y - e^-x.e^y + e^-x.e^-y) = 1/4(2e^x.e^y + ...
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Answered by Alex H. • Maths tutor
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A curve has equation y = (12x^1/2)-x^3/2

y = 12x 1/2 - x 3/2 First take the 1/2 power and multiply by the integer in front of the x (so 12 x 1/2 = 6), then minus 1 from the power (1/2 - 1 = -1/2) and replace the power above the x with -1/2. So that...
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Answered by Amay B. • Maths tutor
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Find the stationary point of the function f(x) = x^2 +2x + 5

We can find stationary points of functions by using differentiation, we start this by assessing each term individually, we start with the first term x 2 , we first start by taking the power term (2 in this c...
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Answered by Henry O. • Maths tutor
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œintegrate xe4x in respect to x

1/4xe^4x-1/16e^4x +c
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Answered by M A. • Maths tutor
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The point on the circle x^2+y^2+6x+8y = 75 which is closest to the origin, is at what distance from the origin? (Taken from an MAT paper)

This is a good example of a question where intuition about geometry is important. Completing the square is a standard A level practice to find the equation of a circle. Doing this we get (x+3) 2 -9 +(y+4) 2 ...
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Answered by Jack M. • Maths tutor
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