MATH 139 Midterm: MATH139 Winter 1999 Exam

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

Document Summary

189-139b: (15 marks) compute the following limits. (a) lim x 0 tan(2x) sin(7x) (b) lim h 0+ H q4 + h 2 (c) lim x 1 x3 1 x2 1. 2. (a) (15 marks) di erentiate the following functions: f (x) = (ln (x2 + 1)) 4x (b) compute dy dx x2 sin y = x3 + y3. 2 e x + ey = 3 ex y at the point (0,0). (c) the volume of a spherical balloon is being increased at the rate 3cm3/sec. 189-139b: (30 marks) sketch the graph of f (x) = x + 2 + 4 x 2 indicating where the function is increasing, decreasing, concave up, concave down, has local maxima, local minima, in ection points, and asymptotes (if they exist). 5. (a) (15 marks) show that the function f (x) = ( (x 1)3. Explain. if x 1 if x > 1.