MATH 139 Midterm: MATH139 Fall 2000 Exam

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 139
• Professor: All

Document Summary

Mathematics 189-139a: (9 marks) find the following limits. You may use l"hospital"s rule if you wish. (a) limx 3. 2e2x + 5 (c) limx 0 arctan x x: (9 marks) find the derivative of each of the following functions (a) f(x) = 4x + 3 (b) f(x) = 5. (i) (4 marks) find all the critical points of the function f(x) = cos x + x sin x in the interval . Mathematics 189-139a: (10 marks) find the point on the line 2x + y = 3 nearest to the point (5, 8). (hint : Find the angle at the apex of the sector that maximizes the area of the sector. (hint : The area of a sector is given by the formula r2 where the radius is r metres and . 2 is the angle at the apex, i. e. between the two radii. ) r r r.