SULIT BA601: ENGINEERING MATHEMATICS 5

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1 SECTION A BAHAGIAN A INSTRUCTION: This section consists of TWO () questions with 5 marks each. Answer ONE (1) question from each part, and ONE (1) remaining question from either part A/B/C ARAHAN : Bahagian ini mengandungi DUA () soalan dengan jumlah 5 markah setiap soalan. Jawab SATU (1) soalan dari setiap bahagian, dan SATU (1) soalan selebihnya dari mana-mana bahagian samada A/B/C. QUESTION 1 SOALAN 1 C (a) Find the value for each of the following by using the definition/formula of hyperbolic functions: Cari nilai bagi setiap yang berikut dengan menggunakan definisi/formula fungsi hiperbolik. i. cosh 8 [ marks] [ markah] tanh.5 [ marks] [ markah] i sinh 1 ln [ marks] [ markah] iv. cosech 1 3 [ marks] [ markah] SULIT

2 (b) Prove that Buktikan bahawa i. cosh x sinh x e cosha B cosh Acosh B sinh Asinh B x [3 marks] [3 markah] C (c) Sketch a quadrant graph and find the principal value for the following functions: Lakarkan graf sukuan dan dapatkan nilai utama bagi fungsi-fungsi berikut: i. cos tan SULIT

3 QUESTION SOALAN (a) Find the value for each of the following by using the definition/formula of hyperbolic functions: Cari nilai bagi setiap fungsi yang berikut dengan menggunakan definisi/formula fungsi hiperbolik: v. sinh ln 5 C vi. sech v cosh 1 coth 4 (b) Complete the table below for equation range of 4 x 4. [ marks] [ markah] [ marks] [ markah] x y sinh. Then sketch the graph in the 3 Lengkapkan jadual di bawah bagi persamaan graf pada julat 4 x 4. x y sinh. Seterusnya lakarkan 3 x y 4 SULIT

4 (c) Given that Diberi x cosh x sinh x me, find the value of m. x cosh x sinh x me, cari nilai bagi m. (d) Prove that 1 1 x tanh 1 x ln 1 x Buktikan 1 1 x tanh 1 x ln 1 x [8 marks] [8 markah] 5 SULIT

5 SECTION B BAHAGIAN B INSTRUCTION: This section consists of TWO () questions with 5 marks each. Answer ONE (1) question from each part, and ONE (1) remaining question from either part A/B/C ARAHAN : Bahagian ini mengandungi DUA () soalan dengan jumlah 5 markah setiap soalan. Jawab SATU (1) soalan dari setiap bahagian, dan SATU (1) soalan selebihnya dari mana-mana bahagian samada A/B/C. QUESTION 3 SOALAN 3 CLO (a) Differentiate the following functions with respect to x. Bezakan setiap fungsi yang berikut terhadap x. i. tanh 1 x y 4 [3 marks] [3 markah] ln(coshx) y e i cos 1 3x y x CLO (b) Determine dy for the implicit function 3 cosh x ln y x y 5. 6 SULIT

6 Tentukan dy untuk fungsi tersirat 3 cosh x ln y x y 5 [7 marks] [7 markah] CLO (c) Given z 4ycosh3 x 3xsinh y Diberi z 4ykosh3 x 3xsinh y, find, cari z z z z z z,,,, and. x y x y xy yx z z z z z z,,,, and. x y x y xy yx 7 SULIT

7 QUESTION 4 SOALAN 4 CLO (a) Integrate the following functions with respect to x. Kamirkan fungsi-fungsi berikut terhadap x. i. sinh( 9 7x) [3 marks] [3 markah] i 5cosh 3 x sinh x 3 7 ( x ) CLO (b) Solve the following integrals: Selesaikan kamiran yang berikut: 3x i. ( x 3)( x ) x 0 8 SULIT

8 SECTION C BAHAGIAN C INSTRUCTION: This section consists of TWO () questions with 5 marks each. Answer ONE (1) question from each part, and ONE (1) remaining question from either part A/B/C ARAHAN : Bahagian ini mengandungi DUA () soalan dengan jumlah 5 markah setiap soalan. Jawab SATU (1) soalan dari setiap bahagian, dan SATU (1) soalan selebihnya dari mana-mana bahagian samada A/B/C. QUESTION 5 SOALAN 5 CLO3 (a) Form a differential equation for each of the following functions: Bentukkan persamaan pembezaan bagi setiap fungsi yang berikut: i. y Ax 3 6Bx y 4Acoshx 4Bsinh x CLO3 C4 (b) Solve the following differential equations: Selesaikan persamaan pembezaan berikut: y x dy i. e = ex [3 marks] [3 markah] dy = xy x y i x dy + xy = 3x3 [7 marks] [7 markah] 9 SULIT

9 QUESTION 6 SOALAN 6 CLO3 (a) Solve the following differential equations: Selesaikan persamaan pembezaan berikut: i. dy 5x 3 y 7 dy 5y e 5 x CLO3 (b) Solve the following second order of differential equations: Selesaikan persamaan pembezaan peringkat kedua berikut: d y dy i. 9 0y 0 d y dy 14 49y 0 d y dy i 7y 0 SOALAN TAMAT 10 SULIT

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