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McLaurin Expansion - Mathematics - Old Exam Paper

Exams, Mathematics

Post: March 28th, 2013
Description
Main points of this past exam are: Mclaurin Expansion, Places of Decimals, Root Mean Square Value, Find Average Value, Mass Per Unit Length, Differential Equations, Mean Length, Confidence Limits, Normally Distributed
Main points of this past exam are: Mclaurin Expansion, Places of Decimals, Root Mean Square Value, Find Average Value, Mass Per Unit Length, Differential Equations, Mean Length, Confidence Limits, Normally Distributed
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Cork Institute of Technology Higher Certificate in Engineering in Civil Engineering – Award (National Certificate in Engineering in Civil Engineering – Award) (NFQ – Level 6) Summer 2005 Mathematics (Time: 3 Hours) Instructions Answer FIVE questions; a minimum of TWO questions in each of Sections A and B should be attempted. All questions carry equal marks. Examiners: Mr. L. O Hanlon Mr. P. Anthony Mr. J. Murphy Section A Q1. (a) (b) (c) (d) (e) Q2. (a) Differentiate with respect to x: y = e-2x + 4x y = eSin x x –y –x y =0 x = a (Cost + bSint) y = c(Sint + dCost) y = xSinx Write down the first four terms of the McLaurin expansion of f(x) = ex. Hence calculate e .1 correct to four places of decimals. (b) Q3. (a) Find the maximum and minimum values of y = lnx – x2 + 2x. Integrate (10 Marks) (10 Marks) a,b,c,d are constants (4 Marks) (4 Marks) 3 3 3 3 (4 Marks) (4 Marks) (4 Marks) ∫ 1 0. 5 ex − 1 1 dx x2 dx (4 Marks) (4 Marks) (4 Marks) (b) (c) (d) (e) ∫ 16 + x..

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