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Use the binomial series to find the expansion of 1/(2+5x)^3 in ascending powers of x up to x^3 (|x|<2/5)

We want to rearrange the expression to the form (1+y)^n so we can use the general result: (1+y)^n=1+ny+[n(n-1)/2]y^2+[n(n-1)(n-2)/3!]y^3+... 1/(2+5x)^3 = (2+5x)^-3 = [2(1+5x/2)]^-3 = (2^-3)(1+5x/2)^-3 usi...

Answered by Saskia J. • Maths tutor

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differentiate y=(5x-2)^5

25(5x-2)^4

Answered by Miss K. • Maths tutor

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Find the gradient of the curve (x^3)-4(y^2)=12xy at the point P(-8,8)

First of all differentiate the equation of the curve implicitly, giving:

3x²-8y(dy/dx)=12y+12x(dy/dx)

=> (dy/dx)(12x+8y)=3x²-12y

=> dy/dx=(3x²-1...

Answered by Franco Guglielmo R. • Maths tutor

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whats the integral of x.e^x wrt x

e^x(u-1)

Answered by Peter C. • Maths tutor

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An open-topped fish tank is to be made for an aquarium. It will have a square base, rectangular sides, and a volume of 60 m3. The base materials cost £15 per m2 and the sides £8 per m2. What should the height be to minimise costs?

Establish the areas of each of the five faces of the aquarium in terms of x and y, and then sum to obtain a function of the cost in x and y. Then identify that the volume also gives a function in x and y....

Answered by Jonny P. • Maths tutor

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