846
Answer Key
244.12 minutes. 6.43 . At 5% interest, she must invest $223,130.16. At 6% interest, she must invest $165,298.89. 6.44 . 38.90 months 6.45 . The coffee is first cool enough to serve about 3.5 minutes after it is poured. The coffee is too cold to serve about 7 minutes after it is poured. 6.46 . A total of 94.13 g of carbon remains. The artifact is approximately 13,300 years old. 6.47 . a. d dx ⎛ ⎝ tanh ⎛ ⎝ x 2 +3 x ⎞ ⎠ ⎞ ⎠ = ⎛ ⎝ sech 2 ⎛ ⎝ x 2 +3 x ⎞ ⎠ ⎞ ⎠ (2 x +3)
⎛ ⎝ ⎜ 1
⎞ ⎠ ⎟ = d
d dx
x ) −2 =−2(sinh x ) −3 cosh x
dx (sinh
b.
(sinh x ) 2
6.48 .
a. ∫ sinh 3 x cosh xdx = sinh 4 x 4 + C b. ∫ sech 2 (3 x ) dx = tanh(3 x ) 3 + C
6.49 .
⎛ ⎝ cosh −1 (3 x ) ⎞
d dx
⎠ = 3
a.
9 x 2 −1
2
⎛ ⎝ coth −1 x ⎞ ⎠
3
3
⎛ ⎝ coth −1 x ⎞ ⎠
d dx
b.
=
1− x 2
6.50 .
⎛ ⎝ x 2
⎞ ⎠ + C
a. ∫ 1
dx =cosh −1
x 2 −4
b. ∫
1 1− e 2 x
dx =−sech −1 ( e x )+ C
6.51 . 52.95ft Section Exercises 1 . 32 3 3 . 13 12 5 . 36 7 .
243 square units 9 .
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