844
Answer Key
429 . 1 ⎞ ⎠ 431 . 1− 2 5 2 ln ⎛ ⎝ 4 3
433 . 2tan −1 ( A )→ π as A →∞ 435 . Using the hint, one has ⌠ ⌡
dx = ⌠ ⌡
csc 2 x csc 2 x +cot 2 x
csc 2 x 1+2cot 2 x
dx . Set u = 2cot x . Then, du =− 2csc 2 x and the ⎠ + C . If one uses the identity tan −1 s +tan −1 ⎛ ⎝ 1 s ⎞ ⎠ = π 2 ,
⌠ ⌡
du 1+ u 2
tan −1 ⎛
⎝ 2cot x ⎞
tan −1 u + C = 1 2
integral is − 1 2
= − 1 2
then this can also be written 1 2 ⎞ ⎠ + C . 437 . x ≈ ±1.7321. The left endpoint estimate with N =100 is 4.781 and these decimals persist for N =500. Review Exercises tan −1 ⎛ ⎝ tan x 2
439 . False 441 . True 443 . L 4 =5.25, R 4 =3.25, exact answer: 4 445 . L 4 =5.364, R 4 =5.364, exact answer: 5.870 447 . − 4 3 449 . 1 451 . − 1 2( x +4) 2 + C 453 . 4 3 sin −1 ⎛ ⎝ x 3 ⎞ ⎠ + C 455 . sin t 1+ t 2 457 . 4 ln x x +1 459 . $6,328,113
461 . $73.36 463 . 19117
12 ft/sec, or 1593 ft/sec
Chapter 6 Checkpoint 6.1 . 12 units 2 6.2 . 3 10 unit 2 6.3 . 2+2 2 units 2 6.4 . 5 3 units 2 6.5 . 5 3 units 2 6.7 . 6.8 . 8 π units 3 6.9 . 21 π units 3 6.10 . 10 π 3 units 3 6.11 . 60 π units 3 6.12 . 15 π 2 units 3 6.13 . 8 π units 3 π 2
This OpenStax book is available for free at http://cnx.org/content/col11964/1.12
Made with FlippingBook - professional solution for displaying marketing and sales documents online