C:/Users/tad/OneDrive - Deakin University/_A_Teaching/SIT194/assignment/SIT194_ASSIGN2.dvi SIT194: Introduction To Mathematical Modelling Assignment 2 (17% of unit) Due date: 8:00pm AEST Thursday, 3...

i need help for assigment


C:/Users/tad/OneDrive - Deakin University/_A_Teaching/SIT194/assignment/SIT194_ASSIGN2.dvi SIT194: Introduction To Mathematical Modelling Assignment 2 (17% of unit) Due date: 8:00pm AEST Thursday, 3 September 2020 Important notes: • Your submission can be handwritten but it must be legible. • All steps (workings) to arrive at the answer must be clearly shown. All formulas from the subject material for the unit can be used - otherwise results must be derived. • Only (scanned) electronic submission would be accepted via the unit site (Deakin Sync). • Your submission must be in ONE pdf file. Multiple files and/or in different file format, e.g. .jpg, will NOT be accepted. • Question marked with a * are harder questions. Questions 1. For following functions, (a) identify the basic function, (b) identify the sequence of the trans- formation and (iii) sketch (without using any computer aids) their graphs showing key points: (i) f(x) = 1 + r(x+ 1), where r(x) is the ramp function (ii) f(x) = 1− √ 1− x (5 marks) 2. Determine the following derivatives: (i) d dx ( ∫ x 2 t2 sin t dt ) (ii) d dr ( ∫ r 0 √ x2 + 4 dx ) (iii) d dx ( ∫ 1 x cos √ t dt ) (iv) d dx ( ∫ x2 tanx 1 2 + t4 dt ) (4 marks) 3. Evaluate the following integrals: (a) I = ∫ x(2x2 + 3)1/3 dx (b) I = ∫ (6x+ 5)e2x dx (c) I = ∫ 1 (9− x2)1/2 dx (d) I = ∫ −x+ 27 x2 + x− 30 dx (e) I = ∫ sin θ 2 cos2 θ + 4 cos θ + 20 dθ (12 marks) 4. Solve the following differential equations: (a) dy dx = xy1/2; y(0) = 4 (b) dy dx − 2y x = x2; y(1) = 2 (6 marks) 5. * If ∫ 4 0 e(x−2) 4 dx = k (k is a constant), find the value ∫ 4 0 xe(x−2) 4 dx (2 marks) 6. * If ∫ xα 0 f(t)dt = [f(xα)]2, where α is a positive constant, determine f(x). (2 marks) 7. * Evaluate the following integral I = ∫ x sin−1 x dx (3 marks)