Analyse the engineering situations and solve engineering problems using calculus

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Calculus

Asked: Jan 4th, 2018

Question Description

If the volume of a circular cylindrical block is equal to 750 cm³show that the total surface area = 2π x²+ 1500/x cm² where x cm is the radius of the base. Hence obtain the value of x which makes the surface area a minimum.
Determine the volume of revolution formed by rotating the area enclosed by the curve y = 3/x, the x-axis and the lines x = 1 and x = 2 through 360 degrees about the x-axis. Sketch the volume generated by this revolution

Determine higher order derivatives for algebraic functions in part a)

The displacement of a particle in simple harmonic motion is given by x = A cos(ωt) + B sin(ωt) where ω represents the angular frequency and A and B are constants. Show that d^2x/dt^2 + ω²x = 0

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Analyse the following engineering situations and solve engineering problems using calculus giving your answers to 4 decimal places. a) If the volume of a circular cylindrical block is equal to 750 cm3 show that the total surface area = 2π x2 + 1500/x cm2 where x cm is the radius of the base. Hence obtain the value of x which makes the surface area a minimum. b) Determine the volume of revolution formed by rotating the area enclosed by the curve y = 3/x, the x-axis and the lines x = 1 and x = 2 through 360 degrees about the x-axis. Sketch the volume generated by this revolution Determine higher order derivatives for algebraic functions in part a) a) The displacement of a particle in simple harmonic motion is given by x = A cos(ωt) + B sin(ωt) where ω represents the angular frequency and A and B are constants. 𝑑2 𝑥 Show that 𝑑𝑡 2 + ω2x = 0

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