University of MD University College Calculus II - Math 141 Final Exam (100 pts) Dr. Ahmed Mohamed Summer 2017 08/10/2017 (The final exam is comprehensive. Show all your work to get full credit) 6. (10 pts each) Evaluate the following integrals. tan 3 x sec x dx 2x3 4x 8 x 2 x x 2 4 dx 2. (10 each) x2 3 3 x dx dx x 2 1 3 / 2 2 ex 2 x dx 1 e Find the power series for . f ( x) 1 x 3 3. (10 pts) Find the first three nonzero terms of the McLaurin series for the function f ( x ) e x arctan x . 4. (10 pts) Find the McLaurin series for the function 5. (10 pts) Use a Taylor polynomial with n = 8 (degree of the polynomial) to approximate f ( x) x cos x . 1 cos x dx . 2 1 6. (10 pts) Use a power series to approximate (the first nonzero four terms) of 1 x2 e dx . 0 Have a great summer break