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Maths Practice
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School of computing, science and Engineering
Engineering Mathematics E1 CRN: 31886
Phase Test 2
Date: Tuesday 1/4/2014 Time:10:00-11:30 hrs
Instructions to Candidates
Formulae sheets are appended to this paper
Approved electronic calculators may be used.
1.(a)Differentiate the following functions with respect to x:
(i),(4 marks)
(ii),(4 marks)
(iii).(4 marks)
(b)A curve is given by the parametric equations:
.
Determine expressions for in terms of t.
(8 marks)
2.(a)If show that
.(12 marks)
(b)The base radius of a cone, r, decreases at a rate of 0.1cm/sec while the perpendicular height, h, increases at a rate of 0.2cm/sec. Calculate the rate at which the volume, v, changes when r = 1.5cm and h = 2.5cm.(8 marks)
3.(a)Solve the following hyperbolic function, giving your answer correct to four decimal places:
.(6 marks)
(b)Prove that .(8 marks)
(c)Use the hyperbolic substitution to determine the following definite integral:
.
(6 marks)
4.(a)If show that:
.
(6 marks)
(b)Use the double angle formula to evaluate the integral;
(6 marks)
(c)Express in partial fractions and hence evaluate:
(8 marks)