MATH 141 Midterm: MATH 141 McGill Examf98

• School: McGill University
• Department: Mathematics and Statistics
• Course: MATH 141
• Professor: All

Document Summary

Read directions carefully and show all your work. Partial credit will be assigned based upon the correctness, completeness, and clarity of your answers. Correct answers without proper justi cation or those that use un- approved short-cut methods will not receive full credit. If you use a calculator to help nd an answer, you must write down enough information on what you have done to make your method understandable. Give exact answers unless otherwise noted: (20 pts. ) Evaluate the following integrals. (a) z e2xex dx (b) z sin2 x cos3 x dx (c) z arctan x dx. 1 (d) z x (1 + x2)3/2 dx: (8 pts. ) The maclaurin series for ln(1 + t) = of the maclaurin series for f (x) = ln(1 + 2x) x ( 1)k+1tk k. Find the interval of convergence for the series. 3(2x 3)k k 7k: (8 pts. ) Solve the initial value problem dy dx x2 + 2.