Answer Format Unless otherwise noted, enter answers as: - Whole Numbers - Exact Fractions (e.g., 2/3 or -5/4) or (only when necessary): - Decimals correct to six decimal places The use of decimal numbers is discouraged because decimal numbers are subject to rounding errors, which could cost you marks! Topics: Sections 7.5 and 7.8 in the textbook. Problem #1: Evaluate the following integral. x cos 2x dx Problem #1: Enter your answer symbolically, as in these examples Just Save Submit Problem #1 for Grading Problem #1 Attempt # 1 Attempt #2 Attempt # 3 Your Answer : Your Mark: Problem #2: Evaluate the following integral. Problem #2: Enter your answer symbolically, as in these examples Just Save Submit Problem #2 for Grading Problem #2 Attempt # 1 Attempt #2 Attempt # 3 Your Answer : Your Mark: Problem #3: Evaluate the following integral. cos x sin' x dx Problem #3:Problem #4: Evaluate the following improper integral. 00 ev; dx l2. 7; Ifthe integral does not converge, then write "divergent". Enter your answer symbolically, If the integral does not converge Problem #4- l:las in these examples - - ' then write "divergent". l Just Save l l Submit Problem #4 for Grading Problem #4 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #5: Evaluate the following improper integral. 75x Ifthe integral does not converge, then write "divergent". . Enter your answer symbolically, If the integral does not converge Problems. I:I.,.int...s....,........es - - ' then write "divergent". l Just Save l l Submit Problem #5 for Grading Problem #5 Attempt #1 Attempt #2 Attempt #3 Your Answer: Your Mark: Problem #6: Use the Comparison Theorem to determine which of the following integrals converge. arctanxdx (0 f at + 2 00 x8_ (ii) L \\l x6 2 dx M2 2 + sinxdx (1")x1a (A) all of them (B) (ii) and (iii) only (C) (i) and (iii) only (D) (i) only (E) (i) and (ii) only (F) (i) only (G) none of them (H) (ii) only Problem #6: Answer Format Unless otherwise noted, enter answers as: - Whole Numbers - Exact Fractions (e.g., 2/3 or -5/4) or (only when necessary): - Decimals correct to six decimal places The use of decimal numbers is discouraged because decimal numbers are subject to rounding errors, which could cost you marks! Topics: Sections Appendix E (Mathematical Induction), 11.1, and 11.2 in the textbook. Problem #1: Suppose that a sequence is defined by a1= 1, an+1 = 3 ( an + 4 ). To show that an is monotonic using mathematical induction, which of the following would be the second step? (A) Assume ak S ax+ 1 and show that 3 (ak+ 1 + 4) = 3 (ax+ 2 + 4) (B) Assume (ak+ 1 + 4)