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Find the area between the curves C_1, C_2 and the lines x=0 and x=1, where C_1 is the curve y = x^2 and C_2 is the curve y = x^3.

We start by drawing a diagram which illustrates the question. First draw the x-y plane and the two curves curve y = x^2 and y = x^3. Notice that the two curves intersect at x=0 and x=1, and in the range ...

Answered by Monika K. • Maths tutor

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Find the coordinates of the stationary points y=x^4-8x^2+3

Begin with the equation: y = x⁴-8x²+3. Differentiate by bringing the power down and reducing the power by 1 of each of the terms with x in and constant terms (3) become zero. dy/dx =...

Answered by Finlay H. • Maths tutor

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If the function f is defined as f= 1-2x^3 find the inverse f^-1

Set the function equal to y so y=1-2x^3now rearrange this to set x as the subject 2x^3= 1-yx^3 = (1-y)/2x = ((1-y)/2)^1/3therefore the inverse is f^-1 = ((1-x)/2)^1/3

Answered by Kavita K. • Maths tutor

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Differentiate y=x^2cos(x)

This is done using the product rule: dy/dx=udv/dx +vdu/dxset y=uv therefore u=x^2 v=cos(x)differentiate these with respect to x du/dx= 2x as you multiply by the power and then subtract the power by 1dv/dx...

Answered by Kavita K. • Maths tutor

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I don't understand how to visualise differentiation, please could you show my an example to allow me to understand what it actually is better?

Well first, we could start with a straight line y = x. You should remember from GCSE that the equation of a straight line is given by y = mx + c, where m here is equal to 1.

Answered by Daniel W. • Maths tutor

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