M 160 - Self-study Assignments – Chapters 6 & 7

Section / Self-Study Book Exercises
6.1 / #1, 3, 5, 16, 17, 19, 25, 27, 37, 39, 43, 45, 47, 51, 57, 61
6.2 / #5, 7, 9, 11, 13 (Draw and shade graphs for each.), 22

6.1 #16

6.2#22 (a) 32 ft (b) 37 ft (c) 36 ft


Section / Self-Study Book Exercises
6.3 / #1, 3, 5, 7, 8, 9, 11, 13, 15, 17, 19, 25, 29, 30 (#29 & #30 Sketch and shade a picture of the area being found.), 35, 36 (#36 explain why), 37, 41, 43
6.4 / #5, 6, 7 – 15 odd, 16, 17, (Sketch and shade a picture of the area being found for each problem.)
#19 (You will need a different sketch/shading for each part.)

6.3#8, 1; #30 2

#36 negative, since there is more area below the x-axis than above it

6.4#6, 16/3; #16, 4/3


Section / Self-Study Book Exercises
6.5 / #1, 3, 5, 7, 8, 10, 11, 12
#31 – 34, 36 (Remember to sketch each problem.)
6.6 / #1 – 4, 9, 10, 14, 15, 32, 37
#5 – 8, 11, 12, 13, 16, 17, 18, 19, 33, 36, 37 (#17 alternate answer below)

6.5

#8, 5.1548#10, $171.83#12, $173.33#32, (99/100) pi#34, (16/15) pi#36, (13/3) pi

6.6

#2, (1/3) (x^3+1)^3 + C#4, (2/3) (x^2+3)^(3/2) + C#6, -e^(-x^2) + C#8, (1/7) (x^2+x+3)^7 + C

#10, (2x+1)^(1/2) + C#12, (1/3) ln(e^(3x)+1) + C#14, (1/2) (ln x)^2 + C

#16, (1/2) e^( x^2+2x+4) + C#17, (3/2) ln /2x-4/ + C #18, 2e^(sqrt(x)) + C

#32, (1/3) (x^2-1)^(3/2) + C#36, (1/3) ln/3x^2-3x+1/ + C


Section / Self-Study Book Exercises
7.1 / #1, 4, 3, 5, 6, 11, 15, 17, 21
7.2 / #1, 3, 5, 7, 9, 11
#15, 17, 21, 27, 29

7.1 #4, e^sqrt(2); 4e^5#6, 6+2k – 6 = 2k


Section / Self-Study Book Exercises
7.3 / #7, 17 – 25 odd, 26
7.4 / #1, 3, 4, 5

7.37.4

#26 (0,0) neither; (-2, 1) rel. min.; (2, -1) rel. min.#4 minimum is -3 at (3, 8)