Math辅导 | SIT194 Introduction To Mathematical Modelling Assignment 1

SIT194: Introduction To Mathematical Modelling
Assignment 1 (10% of unit)
Due date: 11:00pm AEST Thursday, 1 August 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. Determine if the following functions are even, odd or neither. (i) f(x) = x3−2x
5×4 −x2
(ii) f(x) = sin?x6−2×2 ?
x4 +2×2
2. Forthefunctiony=f(x)=|2x+3|,
(i) Determine the domain and range of the function.
(ii) Clearly sketch the function showing important points, i.e. intercepts. (iii) Find a restriction of the domain such that the function is one-to-one.
3. Evaluate the following limits: (i)
(2 marks)
(3 marks)
lim x2 − 3x − 18 x→−3 x2 +8x+15
lim 6×3−4x+7 x→∞ 5−2×2 −3×3
(4 marks)

4. Find the derivative of the following functions: (i) y = (xex + sin x)7
(ii) y = (x3 + x) sin−1 x
5. Using implicit differentiation, determine dy if dx
sin(yx) = y2
6. Using logarithmic differentiation, determine dy if dx
y = (x4 −3×3 +5)1/3 (x3 − 7×2)2/5
(4 marks)
(3 marks)
(3 marks)
(2 marks)
7. *Is there a number b such that
exists? If so, find the value of b and the value of limit.
lim x2 +2bx−b−2 x→1 x2 − 4x + 3
8. *For the curve x2 + xy + y2 = 6, find the points where tangent is parallel to the (a) x-axis; (b) y-axis.
(3 marks)