Mat2691 mathematics ii Study guides, Class notes & Summaries
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MAT2691 ASSIGNMENT 1 SOLUTIONS 2023 UNISA ENGINEERING MATHEMATICS II
MAT2691-Mathematics II (Engineering) Assignment 01 Solutions with clear step by step calculations
![MAT2691 - Mathematics II EXAM PREP.](/docpics/6210b8239dd4d_1574049.jpg)
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MAT2691 - Mathematics II EXAM PREP.
- Exam (elaborations) • 29 pages • 2022
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8.8.1 Preparation Paper I (May/June 2010) 
Question 1 
Determine the following integrals: 
1.1 2 2 sin x x dx (2) 
1.2 
2 2 
1 
n x dx (5) 
1.3 2 9 4 
dx 
 x 
 
 (4) 
1.4 
2 27 6 
x dx x x 
 
 
 (7) 
 [18] 
Question 2 
2.1 Determine the root-mean-square value (RMS) of 2 
1 
1 
y 
x 
 
 
 
 between x 0 and x 3 . (8) 
2.2 Calculate the volume of the cone generated by revolving the area 
 between y x 2 , the y -axis and the line y 5 abou...
![MAT 2691 - INTEGRATION: Trigonometric Functions & Hyperbolic Functions](/docpics/626dbfafb1e4e_1709539.jpg)
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MAT 2691 - INTEGRATION: Trigonometric Functions & Hyperbolic Functions
- Other • 6 pages • 2022
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MAT 2691 - 
INTEGRATION: 
Trigonometric Functions 
& Hyperbolic Functions | Corresponding to each trigonometric (or hyperbolic) differentiation formula is an integration formula. Although these 
are always given in a formula sheet, it will help you a great deal in the exam in terms of saving time if you learn the 
formulas by heart.
MAT2691 - Mathematics II (Engineering) Assignment 01 Solutions
![MAT2691-Mathematics II Assignment 01 Semester 2 2022.](/docpics/62ee2e868e5e2_1885617.jpg)
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MAT2691-Mathematics II Assignment 01 Semester 2 2022.
- Exam (elaborations) • 5 pages • 2022
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MAT2691-Mathematics II Assignment 01 Semester 2 2022. QUESTION 1 
Determine 
dx 
dy of the following and simplify if possible. 
 
3 2 
2 3 2 
3 2 2 
2 2 
3 
1.1 implicit differentiation 
3 2 1 
2 1 3 
1 3 
2 
x y xy x 
dy dy 
x y x y x y 
dx dx 
dy 
x xy x y y 
dx 
dy x y y 
dx x xy 
 
 
 
 
 
 
 
 (5) 
 
 
2 
2 
2 
2 
1.2 8 logarithmic differentiation...
![MAT2691 Assignment 1 2022](/docpics/62bebfcad83bd_1826020.jpg)
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MAT2691 Assignment 1 2022
- Exam (elaborations) • 5 pages • 2022
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MAT2691 Assignment 1 2022. 
MAT2691 - Mathematics II 
Determine 
dx 
dy of the following and simplify if possible. 
 
3 2 
2 3 2 
3 2 2 
2 2 
3 
1.1 implicit differentiation 
3 2 1 
2 1 3 
1 3 
2 
x y xy x 
dy dy 
x y x y x y 
dx dx 
dy 
x xy x y y 
dx 
dy x y y 
dx x xy 
 
 
 
 
 
 
 
 (5) 
 
 
2 
2 
2 
2 
1.2 8 logarithmic differentiation 
(8 ) 
1 8...
![MAT2691 - Mathematics II Assignment 01 Semester 2 2022.](/docpics/627f16fb82772_1731167.jpg)
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MAT2691 - Mathematics II Assignment 01 Semester 2 2022.
- Exam (elaborations) • 5 pages • 2022
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MAT2691 - Mathematics II Assignment 01 Semester 2 2022. Assignment 01 Semester 2 
This assignment contributes 40% to your year mark. 
QUESTION 1 
Determine 
dx 
dy of the following and simplify if possible. 
 
3 2 
2 3 2 
3 2 2 
2 2 
3 
1.1 implicit differentiation 
3 2 1 
2 1 3 
1 3 
2 
x y xy x 
dy dy 
x y x y x y 
dx dx 
dy 
x xy x y y 
dx 
dy x y y 
dx x xy 
 
 
 
 
 
 
 
...
MAT2691: Mathematics II (Engineering) Assignment 01 Solutions with clear step by step calculations
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