MA211 Exam.pdf - MA 211 ADVANCED CALCULUS Faculty of...

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MA 211: ADVANCED CALCULUS Faculty of Science, Technology & Environment School of Computing, Information & Mathematical Sciences Final Examination Semester 1, 2018 Mode: Face-to-Face/OnlineDuration of Exam: 3 hours + 10 minutes Reading Time: 10 minutes Writing Time: 3 hours Total Marks: 100 INSTRUCTIONS: 1.There are six (6) questions and ALL are compulsory. 2.There are six (6) pages (including this cover page) in this exam paper. 3.Write your answers in the answer booklet provided. Start each question on a new page. 4.Show all necessary working. Partial marks will be awarded for partially correct answers. 5.Only non-programmable calculators are allowed. 6.Some formulas are given on Pages 5 - 6. 7.This exam is worth 50% of your overall mark. The minimum passing mark is 40/100.
Question 1.Start on a new page. Total marks: 5+(3+3)+5+5 = 21.(a) Sketch the natural domain of the functionf(x, y) = ln (4-x2-y2).Use solid lines forportions of the boundary included in the domain and dashed lines for portions not included.(b) Supposez= cos(uv);u=exy;v=x2.Use the chain rule, after drawing an appropriate “treediagramme”, to find∂z∂xand∂z∂y.(c) Find parametric equations of a line through the origin and parallel to the linex= 1-t, y= 2, z= 3 + 4t.(d) Determine whether or not the following limit exists. If the limit exists, find its value.lim(x,y)(0,0)1-cospx2+y2x2+y2.

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