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Find the stationary points of the curve y (x)= 1/3x^3 - 5/2x^2 + 4x and classify them.

To find the stationary points of the curve y(x), you must first differentiate the equation for y(x) in terms of x. This gives d(y(x))/dx = x^2 -5x +4. Now set this differential equal to zero and solve for...

Answered by Danny R. • Maths tutor

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Find the indefinite integral of x^8*ln(3x) using integration by parts

For this method we need to choose our u and dv/dx. Using the Late method (Logarithm, algebra, trigonometric, exponential), we can pick our u value which will be ln(3x). du/dx is therefore 1/x, using the c...

Answered by Joel B. • Maths tutor

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A curve has an equation: (2x^2)y +2x + 4y – cos(piy) = 17. Find dy/dx

You must differentiate each individual term in the equation.Firstly start with the term of the product of 2x² * y, using the product rule (dy/dx = udv/dx + vdu/dx)Let u = 2x²

Answered by Matthew B. • Maths tutor

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A curve f(x,y) is defined by sin(3y)+3ye^(-2x)+2x^2 = 5. Find dy/dx

In questions where we have a function of x and y equal to a constant, we need to find dy/dx indirectly.We use the formula (df/dx) + (df/dy)(dy/dx) = 0So all we do is differentiate each term in the functio...

Answered by Lewie W. • Maths tutor

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Consider the closed curve between 0 <= theta < 2pi given by r(theta) = 6 + alpha sin theta, where alpha is some real constant strictly between 0 and 6. The area in this closed curve is 97pi/2. Calculate the value of alpha.

Student uses the definition of area [A = 1/2 integral r(theta)^2 d theta], and proceeds using standard integration techniques to give a quadratic solvable for alpha. [alpha^2 = 25] Thus, alpha = 5.

Answered by Graham C. • Maths tutor

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