School of Mathematics
2022 Semester 2
MAT1841 Continuous Mathematics for Computer Science

Assignment 2

The assignment is to be submitted via MOODLE via 11:55 pm AEST Friday 16 September 2022.
See the instructions under the assessment tab on MOODLE. Be sure to press the “submit assignment”
button to complete the submission. You must submit a single PDF document no larger than 100MB in
size. It’s the student’s responsibility to ensure that the file is not corrupted.
Assignment 2 is worth 20% of the final mark. There are three questions.
The standard penalty of 10% of the total mark per day will apply for late work.
Show your working. You are required to clearly explain your steps in both English and mathematical
expressions. Most of the marks will be allocated for clear working and explanations. A mathematical
writing guide is available on Moodle.

1. Compute the following derivatives, showing all work as required.
a. Using first principles, differentiate () = −! "⁄ . (Hint: use the ‘difference of
cubes.’)
b. Calculate the second derivative of () = sin(ln(! + 1)). State the domain and
range of (), $() and ′′().
c. Use the inverse method (i.e., the “derivative rule for inverse functions” in §3.3.2 in
the notes) to differentiate ℎ() = tan%&(").
[8 + 6 + 6 marks]

2. Consider the function () = (5 + − !)/(2 − + !) over the domain ∈ [0, 5].
a. Present a graph of the function.
b. Calculate the absolute maximum and minimum of ().
[2 + 12 marks]

3. Consider a curve define parametrically as () = 3 − %& and () = 2 + %&
a. Write the equation of the curve in non-parametric form (i.e. eliminate t between
the two equations.)
b. Find ⁄ in terms of t using parametric differentiation.
c. Find ! !⁄ in terms of t using parametric differentiation.
d. Find the equation of the tangent line to the curve when t = 1.
[4 + 5 + 4 + 3 marks]