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Q2. a) Find the 5th derivative of xʻsin4x (hint: it is simplest to use Liebnitz's theorem)

Q2. a) Find the 5th derivative of xʻsin4x (hint: it is simplest to use Liebnitz's theorem)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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EN1093 Q2. a) Find the 5th derivative of xʻsin4x (hint: it is simplest to use Liebnitz's theorem) b) There is a cylinder with the radius r = 50 cm and the height h = 150 cm. Estimate the change in the volume of the cylinder if the radius decreases by 5 cm and the height increases by 10 cm, based on the Taylor's Theorem. (Note that the volume of a cylinder V = ar?h) The electricity cost of a building equals to the fuel cost of a local diesel generator and the cost of importing electricity from the bulk power grid, expressed by c) C(Pg, Pc) = a + bP, + cP? + dP3 + pPg where C is the electricity cost of the building; P, is the power generation of the local diesel generator; Pc is the amount of electricity imported from the bulk power grid; a, b, c and d are constant fuel cost coefficients; p is the constant electricity price of the bulk power grid. Find the quadratic approximation near the point P, = 20, Pc = 10.
Transcribed Image Text:EN1093 Q2. a) Find the 5th derivative of xʻsin4x (hint: it is simplest to use Liebnitz's theorem) b) There is a cylinder with the radius r = 50 cm and the height h = 150 cm. Estimate the change in the volume of the cylinder if the radius decreases by 5 cm and the height increases by 10 cm, based on the Taylor's Theorem. (Note that the volume of a cylinder V = ar?h) The electricity cost of a building equals to the fuel cost of a local diesel generator and the cost of importing electricity from the bulk power grid, expressed by c) C(Pg, Pc) = a + bP, + cP? + dP3 + pPg where C is the electricity cost of the building; P, is the power generation of the local diesel generator; Pc is the amount of electricity imported from the bulk power grid; a, b, c and d are constant fuel cost coefficients; p is the constant electricity price of the bulk power grid. Find the quadratic approximation near the point P, = 20, Pc = 10.
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