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Closer Value - Mathematics - Exam, Exams of Engineering Mathematics

Dr. Bhim Rao Ambedkar UniversityEngineering Mathematics

Major Points are given below: Mean Diameter, Inverse Laplace Transform, Single Fraction, Deduce, Differential

Typology: Exams

2012/2013

Uploaded on 04/13/2013

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Cork Institute of Technology
Higher Certificate in Engineering in Building Services
Engineering ā€“ Award
(NFQ Level 6)
Autumn 2006
Mathematics
(Time: 3 Hours)
Instructions
Answer FIVE questions.
Question ONE is compulsory.
All questions carry equal marks.
Calculators and log tables may be used.
Examiners: Mr. L. O Hanlon
Mr. D. Leonard
Dr. N. J. Hewitt
Q1. (a) Differentiate y = x2 + Sin x (3 marks)
(b) Y = x3. Cos x (2 marks)
(c) Find the max or min of y = 2x2 ā€“ x + 5 (3 marks)
(d) Integrate dx
x
āˆ«
+
22 4
1 (2 marks)
(e) Evaluate
āˆ«
2
1
3dxx (3 marks)
(f) Find the mean value of y = 2x2 between x = 2 and x = 3. (2 marks)
(g) In a normal problem, the mean Āµ = 12 and the standard deviation, Ļƒ = 2.
Calculate Z where 5.9for =
āˆ’
=x
x
Z
Ļƒ
Āµ
(3 marks)
(h) Evaluate
()()
22
2734 ā‹…ā‹…C (2 marks)
Q2. Differentiate (find dy/dx) for:
(a) y = x2 ā€“ sec x (4 marks)
(b) x
x
ytan
3
= (4 marks)
(c) x3 + y3 + x2 + y2 = O (4 marks)
(d) x = t3 ā€“ 3
Y = t4 + 1 (4 marks)
(e) y = xx (4 marks)
pf3
pf4

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Cork Institute of Technology

Higher Certificate in Engineering in Building Services

Engineering ā€“ Award

(NFQ Level 6)

Autumn 2006

Mathematics

(Time: 3 Hours)

Instructions Answer FIVE questions. Question ONE is compulsory. All questions carry equal marks. Calculators and log tables may be used.

Examiners: Mr. L. O Hanlon Mr. D. Leonard Dr. N. J. Hewitt

Q1. (a) Differentiate y = x^2 + Sin x (3 marks) (b) Y = x^3. Cos x (2 marks) (c) Find the max or min of y = 2x 2 ā€“ x + 5 (3 marks)

(d) Integrate āˆ« x 2 +^1 42 dx (2 marks)

(e) Evaluate āˆ«

2 1

x^3 dx (3 marks)

(f) Find the mean value of y = 2x 2 between x = 2 and x = 3. (2 marks) (g) In a normal problem, the mean (^) Ī¼ = 12 and the standard deviation, (^) Ļƒ = 2. Calculate Z where Z = x āˆ’ Ļƒ^ Ī¼^ for x = 9. 5 (3 marks)

(h) Evaluate 4 C 2 (ā‹… 3 ) (^2 ā‹… 7 )^2 (2 marks)

Q2. Differentiate (find dy/dx) for: (a) y = x^2 ā€“ sec x (4 marks) (b) y = x^3 tan x (4 marks) (c) x^3 + y 3 + x 2 + y^2 = O (4 marks) (d) x = t 3 ā€“ 3 Y = t 4 + 1 (4 marks) (e) y = xx^ (4 marks)

Q3. (a) Given that x = 2 is an approximate root of x^3 ā€“ 4x + 2 = 0, use Newtons method twice to find a closer value. (10 marks) (b) A curve has the equation y = x 4 +^4 x. Show that y has a maximum value of -2. Find its minimum value. (10 marks)

Q4. Integrate:

(a) āˆ« ( x + ) dx

2 1

(^2 4) (4 marks)

(b) āˆ« ( x^2 + 1 ) 3. 2 xdx (4 marks)

(c) āˆ« x Ī» nx dx (4 marks)

(d) āˆ« ( x +^21 x )(āˆ’ x^1 + 2 ) dx (4 marks)

(e) dx

āˆ« 9 āˆ’ x 2

(^1) (4 marks)

Q5. (a) Find the area between the curve y = 3x^2 and the line y = 15x -18 (5 marks) (b) Find the volume of the solid of revolution formed by revolving y = x^3 about the x axis, between x = 2 and x = 3. (5 marks) (c) Find the r.m.s. value of y = 2x 2 ā€“ 1 between x = 3 and x = 4. (5 marks) (d) A body moves under a direct force, given by F = cos x, where x is the distance from the starting point, in metres. Find the total work done in mobbing a distance 2m form the origin (x = 0). (5 marks)