SIT194: Introduction To Mathematical Modelling
Assignment 3 (10% of unit)
Due date: 11:00pm AEST Thursday, 12 September 2019
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 formula discussed in lectures 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. Evaluate the following limit lim e2x −1−2x
x→0 x2
2. Evaluate the following integrals
(i) 􏰁x(x−6) dx
(ii) 􏰁 1 dx x2 + 9
(iii) 􏰁 −3x + 23 dx x2 +x−12
(2 marks)
23 1/2
3. Find the volume formed when the area, on the positive x-axis that is below the curve y = (1 − 2x) and above the x-axis, is rotated about the x axis.
(2 marks)
(6 marks)

4. Solve the following differential equations. (a)
(b)
dy =xy; y(0)=3 dx
dy+2y=x; y(1)=2 dx x
5. Determine whether the following series converges or diverges
􏰀∞ n 3 n=1 e2n
6. (a) Use established MacLaurin series to find the first three non-zero terms of f(x) = e−x2/2
(b) Use your expression in (a) to find an approximation of
􏰁a
x2e−x2/2 dx,
0
(4 marks)
(2 marks)
provided a is within the interval of convergence. Express your approximation as a func- tion of a.
7. *Evaluate the indefinite integral 􏰁 (sin−1 x)2dx
(4 marks)
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