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I I I
Universiti
Malaysia
PAHANG
Engineering • Technology • Creativity FACULTY OF INDUSTRIAL SCIENCES & TECHNOLOGY FINAL EXAMINATION
COURSE :^ CALCULUS
COURSE CODE :^ BUM
LECTURER : NORAZALIZA BINTI MOHD JAMIL
ADAM BIN SAMSUDIN
DATE : 7 JUNE 2016
DURATION : 3 HOURS
SESSION/SEMESTER : SESSION 2015/2016 SEMESTER II
PROGRAMME CODE : BTEIBTM/BTV/BPN
INSTRUCTIONS TO CANDIDATE
- This question paper consists of FIVE (5)^ questions. Answer ALL questions.
- All answers to a new question should start on new page.
- All the calculations and assumptions must be clearly stated.
EXAMINATION REQUIREMENTS
- Scientific calculator 2. APPENDIX
DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO
This examination paper consists of NINE (9)^ printed pages including front page.
CONFiDENTIAL BTEIBTM/BTV/BPN/151611JBUM
QUESTION 1
(a) Indicate whether each of the following statement is^ True (T)^ or False (F).
(i) If a function f(x) is defined at x^ = c,^ then the function is not necessarily
continuous at x = C. (1 Mark) (ii) If^ k^ is any real number, then urn 3x2 =k2. 3 (1 Mark) (iii) If limf(x) does not exist, then f(x) is continuous at x x—c = c. (1 Mark) (iv) All the graph of continuous functions can be drawn without lifting the pen from the paper. (1 Mark)
(b) Evaluate u• rn 8x3+ 2 2x+ (4 Marks)
(c) Evaluate 13x+71-Ix- x-3 (^) x- (5 Marks
CONFIDENTIAL BTE/BTMJBTVIBPN/1516111BUM
(c) Find the value of A so that y = 3x3e_3x^ satisfies the equation
(^2) cfr^ = Axe-'x (6 Marks)
QUESTION 3
(a) (^) The position of a particle moving along a coordinate line is given by
s(t)= t t^2 +4 '^ t>— O where s (^) is in meter and t is in second.
(i) (^) Find the velocity and acceleration functions. (4 Marks) (ii) (^) At what time the particle stops? (2 Marks)
4
CONFIDENTIAL (^) BTE/BTMI13TV/BPN/1516111BUM
(b) (^) Fauzi has a piece of cardboard of dimension of 50 cm by 20 cm as shown in Figure 1. He is going to cut out a square of (^) hx h from every corner and fold up the sides to form a box. Determine the value of (^) h so that the box has the maximum volume. (^50)
Ii / Figure 1 (6 Marks)
(c) Given the function
(^2) +8x+1.
(i) Determine the critical points of this function. (3 Marks) (ii) Sketch the graph of the function in the interval [-1,5]. (5 Marks)
5
x
CONFIDENTIAL (^) BTE/BTMJBTV/BPN/1516IJJT3uM
QUESTION 5
(a) Find the area (^) of the the region between the x —axis and the graph of y (^) = 2x3 from x = (^) —1 to x =1 as shown in Figure 2. Y
Figure 2 (4 Marks)
(b) Sketch the region enclosed by two curves x (^) = 3y2 and x (^) = 2y. Find the volume of the solid obtained by revolving the region about the x - axis. (9 Marks)
(c) (^) Determine the surface area of the solid obtained by rotating y (^) = x2 , 0 :!^ x :^ 1
about the y—axis. (7 Marks)
END OF QUESTION PAPER
V
CONFIDENTIAL BTEIBTM/BTVIBPN/1516111BUM
APPENDIX
Derivatives and Integration of Commonly Used Functions Function Derivatives formulae Integration Formulae
y=f(x) f1(x) ff(x)dx
constant, k 0 lcx + C
x" nx'
n+
-+C, n#-1n+
-^1 - 1 hix+C
ex (^) ex
1n x (^) x 1- xlnx+C sinx (^) cosx —cosx+C cosx (^) —sinx sinx+C tan (^) sec 2 x (^) lnlsecxl+C sec sec x tan x secxtanx + (^) C
Chain Rule dy dy du
dx du dx
If y=u(x).v(x), then —=v dy —+udu --dv
Product Rule dx^ dx^ dx
du dv
Quotient Rule
V--U—
If (^) y=,v(x) then (^) dx AA v
Integration by Parts Judv=uv—Jvdu
