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MAT1841 Continuous Mathematics for Computer Science
创建日期：2024-05-13 15:59:50
所属分类：数学mathematics
标签： MAT1841
Continuous Mathematics for Computer Science

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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]
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关键词一 关键词二 关键词三 关键词四 关键词五 和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 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