# MA211 Exam 2017.pdf - MA211 Advanced Calculus Faculty of...

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MA211: AdvancedCalculus Faculty of Science, Technology and Environment School of Computing, Information and Mathematical Sciences Final Examination Semester I, 2017 Mode: Face-to-Face and Online DurationofExam: 3hours+10minutes Reading Time: 10 minutes Writing Time: 3 hours Total Marks: 100 INSTRUCTIONS: 1. There are 6 questions and ALL are compulsory. 2. Start each question on a new page. 3. There are seven (7) pages (including this cover page) in this exam paper. 4. Show all necessary working. Partial marks will be awarded for partially correct answers. Write legibly. 5. Only non-programmable calculators are allowed. 6. A list of formulae is attached at the end. 7. This exam is worth 50% of your overall mark. To be considered for a clear pass in this course, you must achieve at least 40 out of 100 in this final ex- amination.
MA211 Final Examination Semester I, 2017 Question1: Startonanewpage. ( 4 + 6 + 3 = 13 marks) (a) Show that if A and B are not both zero, then the graph of the polar equation r = A sin θ + B cos θ is a circle. Find its radius. [4 marks] (b) Find the area of the region outside the cardioid r = 2 2 cos θ and inside the circle r = 4. [6 marks] (c) Find parametric equations for the line through the point ( x 1 , y 1 , z 1 ) and parallel to the line x = x 0 + at , y = y 0 + bt , z = z 0 + ct . [3 marks] Question2: Startonanewpage. ( 3 + 4 + 6 = 13 marks) (a) Sketch the graph of f ( x , y )= 4 x 2 y 2 . [3 marks] (b) Evaluate lim ( x , y ) ( 0,0 ) sin ( x 2 + y 2 ) x 2 + y 2 . [4 marks] (c) Given the following information use the Chain Rule to sketch the tree dia- gram and find z u and z v . z = 8 x 2 y 2 x + 3 y , x = uv , y = u v [6 marks] Page 2 of 7
MA211 Final Examination Semester I, 2017 Question3: Startonanewpage. ( 6 + 6 + 6 = 19 marks)