MATH111 Final: Final Exam Fall 2011
Document Summary
A sample has a mass of 10 mg initially. Time: 3 hours: (8 marks) find the limit. Student no. lim x 0 x sin x x3. Page 2: (7 marks) evaluate the integral. Time: 3 hours: (7 marks) evaluate the integral. Page 3: (7 marks) evaluate the integral. Page 4: (7 marks) evaluate the integral. Z 4x2 + x + 2 x3 + x dx. Page 5 (a) determine whether the integral is convergent. 1 e x dx. (b) determine whether the integral is convergent. Page 6: (6 marks) find the length of the curve y = 0 x 5: (8 marks) find the area of the surface obtained by rotating the curve y = 2 x2 (0 x 1) about the y-axis. Page 7: (6 marks) solve the di erential equation dy dx xey2 y(1 + x2) Page 8: (7 marks) solve the initial value problem dy dx.
