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(Solved): QUESTION 5 [15] 5.1 Consider the function f(x) = ex. 5.1.1 Find the first three terms of the Mac ...



QUESTION 5 [15]
5.1 Consider the function f(x) = e¯x.
5.1.1 Find the first three terms of the Maclaurin series expansion of f

QUESTION 5 [15] 5.1 Consider the function f(x) = e¯x. 5.1.1 Find the first three terms of the Maclaurin series expansion of f(x) to four terms. 5.1.2 Deduce the Maclaurin series expansion of f(x) = ex to four terms from the series obtained from 5.1.1 above. (2) 5.1.3 Use your answers in question 5.1.1 and 5.1.2 above to write down a series expansion for cosh x to four non-zero terms. (3) 5.2 Consider the 3 × 3 system of equations with unknown x, y and z given as follows 2x + 4y = 2z = 1 2x + 8y + 4z = 1 30x+12y - 4z = 1. 5.2.1 Write down the constant matrix of this system of equations. (1) (3) 5.2.2 Write down the coefficient matrix of this system of equations. 5.2.3 Calculate the determinant of the matrix given on 5.2.2. (4) (2)


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