ACC 203 Problems For Chapter 7, Fall 2014

LEBANESE AMERICAN UNIVERSITY DEPARTMENT OF COMPUTER SCIENCE AND MATHEMATICS MTH 201 - CALCULUS III Exam-I, Fall 2014 Duration: 75 minutes INSTRUCTIONS: This exam consists of 7 pages and 5 problems. Check that none is missing. Answer the questions in the space provided for each problem; if more space is needed, you may use the back pages. To receive full credits, you have to justify your answers. Student’s Name: Sstuba- Grading scheme (Keep it empty) Question 1 /10 Question 2 /30 Question 3 /30 Question 4 /10 Question 5 /20 Total /100 1. [10 Points] Use partial fractions and evaluate the following integral 40? - 5243 A 4 Bb “ c uy a(x — 1)? 7 x eC 7 2 ¢ te — = Ae) 4 BS be TT x-] 284 +e 3> =? Ale)" ex(x-\)4 Ce = eX A(x 2x+\)* B Kt Bx+C x ~ GK S443 2. [30 Points] Calculate the following improper integrals f 1 a= we QA RK, 1 3. [30 Points] Determine whether the following improper integrals converge or diverge. Justify your answer and precise the test pe are using. oo = [cosa] _ f b (rip = ¢ + } e =) t spams (Ley 6 4. [10 Points] Find the value of a so that the given integral converges °° a 1 [ (a+sH) de ag bee CH TK) KL Xe 2) Ot) ( +1) m4 al fe -1) (x41 Th arz-| => ab => em Vi X V y at -\ >) w 1. —) wav: <> Answar = Get\ * 5. [20 Points] Determine if the following sequences converge or diverge. 7 (a) an = oy . Hint: Use the sandwich theorem. eo () = —™ 6" + 8"