First Semester Examination

2015/2016 Academic Session

Jun 2016

Duration : 3 hour

PPSM, Pusat Pengajian Sains Matematik

Repository@USM

       UNIVERSITI SAINS MALAYSIA  Second Semester Examination 2015/2016 Academic Session   June 2016  MAA101 – Calculus for Science Students I [Kalkulus untuk Pelajar Sains I] Duration : 3 hours [Masa : 3 jam]     Please check that this examination paper consists of SIX pages of printed material before you begin the examination.  [Sila pastikan bahawa kertas peperiksaan ini mengandungi ENAM muka surat yang bercetak sebelum anda memulakan peperiksaan ini.]   Instructions:  Answer SEVEN (7) questions.  [Arahan: Jawab TUJUH (7) soalan].     In the event of any discrepancies, the English version shall be used.  [Sekiranya terdapat sebarang percanggahan pada soalan peperiksaan, versi Bahasa Inggeris hendaklah diguna pakai.]            …2/- [MAA101] - 2 -    1. Find the following limits, if they exist.   (a) 01 1limxxx             (b)   228 16lim4xxx          (c) 2402 7lim3 4xxx                                [ 8 marks ]    1. Dapatkan had berikut, jika ianya  wujud.   (a) 01 1xxhadx              (b) 228 164xxhadx     (c) 2402 73 4xxhadx                                   [ 8 markah ]                                      2. Given      2 , 2, 2 4,2 , 4xf x ax b xx            find the values of a and b if f is continuous everywhere.                              [ 7 marks ]         2. Diberi    2 , 2, 2 4,2 , 4xf x ax b xx          dapatkan nilai-nilai a dan b jika f selanjar di mana-mana.                         [ 7 markah ] …3/- [MAA101] - 3 -    3. (a) Find dydx of the following functions:  (i) 2sin3xy e x    (ii) 2 2 7x xy y      (iii)  21 tan xy x   [ 12 marks ]    (b) A cylindrical swimming pool of height h is being filled with water from a hose at a rate of 1.5 cubic meters per second. How fast is the water level increasing if its radius is 6 meters?  [ 6 marks ]    3. (a)  Dapatkan dydx bagi fungsi-fungsi berikut:   (i) 2sin3xy e x    (ii) 2 2 7x xy y      (iii)  21 tan xy x   [ 12 markah ]     (b) Suatu kolam mandi berbentuk selinder dengan ketinggian h dipenuhi air dari suatu hos pada kadar 1.5 kubik  meter sesaat. Berapakah kadar paras air meningkat jika jejarinya ialah 6 meter. [ 6 markah ]          …4/- [MAA101] - 4 -    4. (a) Consider the equation 3 2 4 0,    1 2x x x     .  (i) Show that by using Newton’s formula, the solutions of the equation can be deduced to  31 22 4,   1,2,3.....3 2nnnxx nx   (ii) Hence, show that the approximated root is 1.17951 correct to 5 decimal places.  [ 9 marks ]    (b) The photosynthesis rate P (mg carbon/m3/h) of phytoplankton, is modelled by the function                                      2100( )4IP II I     where 0I   is the light intensity and measured in thousands of foot-candles. Find the light intensity when P is maximum. [ 8 marks ]    4. (a) Pertimbangkan suatu persamaan 3 2 4 0,    1 2.x x x        (i) Tunjukkan bahawa dengan menggunakan rumus Newton, penyelesaian persamaan ini boleh dideduksikan kepada                  3nn+1 2n2x + 4x = ,  n = 1,2,3.....3x + 2   (ii) Seterusnya, tunjukkan bahawa punca hampiran ialah 1.17951 tepat  kepada 5 tempat perpuluhan. [ 9 markah ]    (b) Kadar fotosintesis P (mg carbon/m3/h) plytoplankton, dimodelkan oleh fungsi                                 2100( )4IP II I    dengan  0I   ialah keamatan cahaya dan diukur dalam beribu kaki-lilin. Dapatkankan keamatan cahaya  apabila P adalah maksimum. [ 8 markah ] …5/- [MAA101] - 5 -    5. Given  22( )4xf xx, find  (a) all asymptotes of  f.  (b) the interval on which  f  is increasing or decreasing.  (c) the local maximum and minimum point, if any.   (d) the interval of concavity and the inflection points, if exist.   Hence, sketch the graph of f.                                                                                                                                [ 20 marks ]    5.  Diberi  22( )4xf xx, dapatkan (a) kesemua asimptot untuk f.  (b) selang bagi  f  menokok atau menyusut.  (c) titik maksimum dan titik minimum tempatan, jika ada.  (d) selang kecekungan dan titik lengkuk balas, jika wujud.   Seterusnya, lakarkan graf  f. [ 20 markah ]                           6. Evaluate the integrals.   (a) cos4 3sinxdxx      (b)  2 5xx x e dx      (c) 1 3202 1 xdxx x                          [ 20 marks ]       …6/- [MAA101] - 6 -    6. Nilaikan kamiran.   (a) cos4 3sinxdxx    (b)  2 5xx x e dx   (c) 1 3202 1 xdxx x          [ 20 markah ]    7. (a) Sketch the region bounded by 22 y x x and y x .    Hence, set up, but do not evaluate the integral for      (i) the area of the region.       (ii) the volume of the solid obtained by rotating the region about the     line 1.x   (b) Set up, but do not evaluate the integral for the length of the curve0cos 2 xy t dt  from 4x   to 1x  .       [ 10 marks ]    7. (a) Lakarkan rantau yang dibatasi oleh 22 y x x dan y x .     Seterusnya, nyatakan kamiran, tanpa menilaikannya untuk       (i) luas rantau.    (ii) isipadu pepejal yang dihasilkan dengan memutar rantau sekitar   garis 1.x             (b)     Nyatakan kamiran, tanpa menilaikannya untuk panjang lengkung 0cos 2 xy t dt  dari 4x  ke 1x  .  [ 10 markah ]      - ooo 0 ooo - 

MAA101 - Calculus For Science Students I [Kalkulus Untuk Pelajar Sains I] Jun 2016

First Semester Examination

Academic Session 2016/2017

December 2016 / January 201

        UNIVERSITI SAINS MALAYSIA  First Semester Examination  Academic Session 2016/2017  December 2016 / January 2017  MAA 101 - Calculus for Science Students I [Kalkulus untuk Pelajar Sains I]   Duration : 3 hours [Masa : 3 jam]      Please check that this examination paper consists of TEN pages of printed materials before you begin the examination.  [Sila pastikan bahawa kertas peperiksaan ini mengandungi SEPULUH muka surat yang bercetak sebelum anda memulakan peperiksaan ini.]   Instructions: Answer EIGHT (8) questions.  [Arahan: Jawab LAPAN (8) soalan.]   In the event of any discrepancies, the English version shall be used.  [Sekiranya terdapat sebarang percanggahan pada soalan peperiksaan, versi Bahasa Inggeris hendaklah diguna pakai].       ...2/- 