University Calculus: Early Transcendentals (4th Edition)
4th Edition
ISBN: 9780134995540
Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.
Publisher: PEARSON
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Chapter 8, Problem 75PE
To determine
The value of the
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(b) Find the (instantaneous) rate of change of y at x = 5.
In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of
change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the
following limit.
lim
h→0
-
f(x + h) − f(x)
h
The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule
defining f.
f(x + h) = (x + h)² - 5(x+ h)
=
2xh+h2_
x² + 2xh + h² 5✔
-
5
)x - 5h
Step 4
-
The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x).
-
f(x + h) f(x) =
= (x²
x² + 2xh + h² -
])-
=
2x
+ h² - 5h
])x-5h) - (x² - 5x)
=
]) (2x + h - 5)
Macbook Pro
Evaluate the integral using integration by parts.
Sx² cos
(9x) dx
Let f be defined as follows.
y = f(x) = x² - 5x
(a) Find the average rate of change of y with respect to x in the following intervals.
from x = 4 to x = 5
from x = 4 to x = 4.5
from x = 4 to x = 4.1
(b) Find the (instantaneous) rate of change of y at x = 4.
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Chapter 8 Solutions
University Calculus: Early Transcendentals (4th Edition)
Ch. 8.1 - Evaluate the integrals in Exercises 124 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...Ch. 8.1 - Evaluate the integrals in Exercises 124 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...Ch. 8.1 - Evaluate the integrals in Exercises 124 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...Ch. 8.1 - Evaluate the integrals in Exercises 124 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...
Ch. 8.1 - Evaluate the integrals in Exercises 124 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...Ch. 8.1 - Evaluate the integrals in Exercises 1–24 using...Ch. 8.1 - Prob. 24ECh. 8.1 - Prob. 25ECh. 8.1 - Prob. 26ECh. 8.1 - Evaluate the integrals in Exercises 25-30 by using...Ch. 8.1 - Prob. 28ECh. 8.1 - Evaluate the integrals in Exercises 25-30 by using...Ch. 8.1 - Evaluate the integrals in Exercises 25-30 by using...Ch. 8.1 - Prob. 31ECh. 8.1 - Prob. 32ECh. 8.1 - Prob. 33ECh. 8.1 - Prob. 34ECh. 8.1 - Prob. 35ECh. 8.1 - Prob. 36ECh. 8.1 - Prob. 37ECh. 8.1 - Evaluate the integrals in Exercises 31–56. Some...Ch. 8.1 - Evaluate the integrals in Exercises 31–56. Some...Ch. 8.1 - Prob. 40ECh. 8.1 - Prob. 41ECh. 8.1 - Prob. 42ECh. 8.1 - Prob. 43ECh. 8.1 - Prob. 44ECh. 8.1 - Prob. 45ECh. 8.1 - Prob. 46ECh. 8.1 - Evaluate the integrals in Exercises 31–56. Some...Ch. 8.1 - Prob. 48ECh. 8.1 - Prob. 49ECh. 8.1 - Prob. 50ECh. 8.1 - Prob. 51ECh. 8.1 - Prob. 52ECh. 8.1 - Evaluate the integrals in Exercises 31–56. Some...Ch. 8.1 - Prob. 54ECh. 8.1 - Prob. 55ECh. 8.1 - Prob. 56ECh. 8.1 - Prob. 57ECh. 8.1 - Prob. 58ECh. 8.1 - Prob. 59ECh. 8.1 - Prob. 60ECh. 8.1 - Prob. 61ECh. 8.1 - Prob. 62ECh. 8.1 - Prob. 63ECh. 8.1 - Prob. 64ECh. 8.1 - Prob. 65ECh. 8.1 - Prob. 66ECh. 8.1 - Prob. 67ECh. 8.1 - Prob. 68ECh. 8.1 - Prob. 69ECh. 8.1 - Prob. 70ECh. 8.1 - Prob. 71ECh. 8.1 - Prob. 72ECh. 8.1 - Prob. 73ECh. 8.1 - Prob. 74ECh. 8.1 - Prob. 75ECh. 8.1 - Prob. 76ECh. 8.1 - Prob. 77ECh. 8.1 - Prob. 78ECh. 8.1 - Prob. 79ECh. 8.1 - Use the formula
to evaluate the integrals in...Ch. 8.1 - Prob. 81ECh. 8.1 - Prob. 82ECh. 8.1 - Prob. 83ECh. 8.1 - Prob. 84ECh. 8.2 - Evaluate the integrals in Exercise 1–22.
1.
Ch. 8.2 - Prob. 2ECh. 8.2 - Evaluate the integrals in Exercise 122. 3....Ch. 8.2 - Evaluate the integrals in Exercise 1–22.
4.
Ch. 8.2 - Evaluate the integrals in Exercise 1–22.
5.
Ch. 8.2 - Evaluate the integrals in Exercise 1–22.
6.
Ch. 8.2 - Evaluate the integrals in Exercise 122. 7. sin5xdxCh. 8.2 - Evaluate the integrals in Exercise 1–22.
8.
Ch. 8.2 - Evaluate the integrals in Exercise 1–22.
9.
Ch. 8.2 - Evaluate the integrals in Exercise 1–22.
10.
Ch. 8.2 - Evaluate the integrals in Exercises 1–22.
11.
Ch. 8.2 - Evaluate the integrals in Exercises 1–22.
12.
Ch. 8.2 - Evaluate the integrals in Exercises 1–22.
13.
Ch. 8.2 - Evaluate the integrals in Exercises 1–22.
14.
Ch. 8.2 - Evaluate the integrals in Exercises 1–22.
15.
Ch. 8.2 - Evaluate the integrals in Exercises 1–22.
16.
Ch. 8.2 - Evaluate the integrals in Exercises 1–22.
17.
Ch. 8.2 - Evaluate the integrals in Exercises 1–22.
18.
Ch. 8.2 - Evaluate the integrals in Exercises 1–22.
19.
Ch. 8.2 - Evaluate the integrals in Exercises 1–22.
20.
Ch. 8.2 - Evaluate the integrals in Exercises 1–22.
21.
Ch. 8.2 - Prob. 22ECh. 8.2 - Prob. 23ECh. 8.2 - Prob. 24ECh. 8.2 - Prob. 25ECh. 8.2 - Prob. 26ECh. 8.2 - Prob. 27ECh. 8.2 - Prob. 28ECh. 8.2 - Prob. 29ECh. 8.2 - Prob. 30ECh. 8.2 - Evaluate the integrals in Exercises 23–32.
31.
Ch. 8.2 - Prob. 32ECh. 8.2 - Evaluate the integrals in Exercises 33–52.
33.
Ch. 8.2 - Evaluate the integrals in Exercises 33–52.
34.
Ch. 8.2 - Evaluate the integrals in Exercises 33–52.
35.
Ch. 8.2 - Evaluate the integrals in Exercises 33–52.
36.
Ch. 8.2 - Evaluate the integrals in Exercises 33–52.
37.
Ch. 8.2 - Evaluate the integrals in Exercises 33–52.
38.
Ch. 8.2 - Evaluate the integrals in Exercises 33–52.
39.
Ch. 8.2 - Evaluate the integrals in Exercises 33–52.
40.
Ch. 8.2 - Evaluate the integrals in Exercises 33–52.
41.
Ch. 8.2 - Evaluate the integrals in Exercises 33–52.
42.
Ch. 8.2 - Evaluate the integrals in Exercises 33–52.
43.
Ch. 8.2 - Evaluate the integrals in Exercises 33–52.
44.
Ch. 8.2 - Evaluate the integrals in Exercises 33–52.
45.
Ch. 8.2 - Evaluate the integrals in Exercises 33–52.
46.
Ch. 8.2 - Prob. 47ECh. 8.2 - Prob. 48ECh. 8.2 - Prob. 49ECh. 8.2 - Prob. 50ECh. 8.2 - Prob. 51ECh. 8.2 - Prob. 52ECh. 8.2 - Prob. 53ECh. 8.2 - Prob. 54ECh. 8.2 - Prob. 55ECh. 8.2 - Prob. 56ECh. 8.2 - Prob. 57ECh. 8.2 - Prob. 58ECh. 8.2 - Prob. 59ECh. 8.2 - Prob. 60ECh. 8.2 - Prob. 61ECh. 8.2 - Prob. 62ECh. 8.2 - Prob. 63ECh. 8.2 - Prob. 64ECh. 8.2 - Prob. 65ECh. 8.2 - Prob. 66ECh. 8.2 - Prob. 67ECh. 8.2 - Prob. 68ECh. 8.2 - Prob. 69ECh. 8.2 - Prob. 70ECh. 8.2 -
Arc length Find the length of the curve
y = ln...Ch. 8.2 - Prob. 72ECh. 8.2 - Prob. 73ECh. 8.2 - Prob. 74ECh. 8.2 - Prob. 75ECh. 8.2 - Volume Find the volume of the solid formed by...Ch. 8.2 - Prob. 77ECh. 8.2 - Prob. 78ECh. 8.3 - Evaluate the integrals in Exercises 1–14.
1.
Ch. 8.3 - Evaluate the integrals in Exercises 1–14.
2.
Ch. 8.3 - Evaluate the integrals in Exercises 114. 3....Ch. 8.3 - Evaluate the integrals in Exercises 1–14.
4.
Ch. 8.3 - Evaluate the integrals in Exercises 114. 5....Ch. 8.3 - Evaluate the integrals in Exercises 1–14.
6.
Ch. 8.3 - Evaluate the integrals in Exercises 1–14.
7.
Ch. 8.3 - Evaluate the integrals in Exercises 1–14.
8.
Ch. 8.3 - Evaluate the integrals in Exercises 114. 9....Ch. 8.3 - Evaluate the integrals in Exercises 1–14.
10.
Ch. 8.3 - Evaluate the integrals in Exercises 1–14.
11. , y...Ch. 8.3 - Evaluate the integrals in Exercises 1–14.
12. , y...Ch. 8.3 - Evaluate the integrals in Exercises 1–14.
13. , x...Ch. 8.3 - Evaluate the integrals in Exercises 1–14.
14. , x...Ch. 8.3 - Use any method to evaluate the integrals in...Ch. 8.3 - Use any method to evaluate the integrals in...Ch. 8.3 - Use any method to evaluate the integrals in...Ch. 8.3 - Use any method to evaluate the integrals in...Ch. 8.3 - Use any method to evaluate the integrals in...Ch. 8.3 - Use any method to evaluate the integrals in...Ch. 8.3 - Use any method to evaluate the integrals in...Ch. 8.3 - Prob. 22ECh. 8.3 - Use any method to evaluate the integrals in...Ch. 8.3 - Use any method to evaluate the integrals in...Ch. 8.3 - Prob. 25ECh. 8.3 - Prob. 26ECh. 8.3 - Use any method to evaluate the integrals in...Ch. 8.3 - Prob. 28ECh. 8.3 - Use any method to evaluate the integrals in...Ch. 8.3 - Use any method to evaluate the integrals in...Ch. 8.3 - Use any method to evaluate the integrals in...Ch. 8.3 - Prob. 32ECh. 8.3 - Use any method to evaluate the integrals in...Ch. 8.3 - Prob. 34ECh. 8.3 - Use any method to evaluate the integrals in...Ch. 8.3 - Prob. 36ECh. 8.3 - Prob. 37ECh. 8.3 - Prob. 38ECh. 8.3 - Prob. 39ECh. 8.3 - Prob. 40ECh. 8.3 - Prob. 41ECh. 8.3 - Prob. 42ECh. 8.3 - Prob. 43ECh. 8.3 - Prob. 44ECh. 8.3 - Prob. 45ECh. 8.3 - Prob. 46ECh. 8.3 - Prob. 47ECh. 8.3 - Prob. 48ECh. 8.3 - For Exercises 49–52, complete the square before...Ch. 8.3 - Prob. 50ECh. 8.3 - For Exercises 49–52, complete the square before...Ch. 8.3 - Prob. 52ECh. 8.3 - Prob. 53ECh. 8.3 - Prob. 54ECh. 8.3 - Prob. 55ECh. 8.3 - Prob. 56ECh. 8.3 - Prob. 57ECh. 8.3 - Prob. 58ECh. 8.3 - Prob. 59ECh. 8.3 - Prob. 60ECh. 8.3 - Prob. 61ECh. 8.3 - Prob. 62ECh. 8.3 - Prob. 63ECh. 8.3 - Prob. 64ECh. 8.4 - Expand the quotients in Exercises 1-8 by partial...Ch. 8.4 - Expand the quotients in Exercises 1−8 by partial...Ch. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - Prob. 7ECh. 8.4 - Prob. 8ECh. 8.4 - In Exercises 916, express the integrand as a sum...Ch. 8.4 - In Exercises 9–16, express the integrand as a sum...Ch. 8.4 - In Exercises 9–16, express the integrand as a sum...Ch. 8.4 - In Exercises 9–16, express the integrand as a sum...Ch. 8.4 - Prob. 13ECh. 8.4 - Prob. 14ECh. 8.4 - In Exercises 9–16, express the integrand as a sum...Ch. 8.4 - Prob. 16ECh. 8.4 - Prob. 17ECh. 8.4 - In Exercises 17–20, express the integrand as a sum...Ch. 8.4 - Prob. 19ECh. 8.4 - Prob. 20ECh. 8.4 - In Exercises 21-32, express the integrand as a sum...Ch. 8.4 - Prob. 22ECh. 8.4 - Prob. 23ECh. 8.4 - In Exercises 21-32, express the integrand as a sum...Ch. 8.4 - Prob. 25ECh. 8.4 - Prob. 26ECh. 8.4 - In Exercises 21-32, express the integrand as a sum...Ch. 8.4 - Prob. 28ECh. 8.4 - Prob. 29ECh. 8.4 - In Exercises 21-32, express the integrand as a sum...Ch. 8.4 - Prob. 31ECh. 8.4 - Prob. 32ECh. 8.4 - In Exercises 33−38, perform long division on the...Ch. 8.4 - Prob. 34ECh. 8.4 - Prob. 35ECh. 8.4 - Prob. 36ECh. 8.4 - Prob. 37ECh. 8.4 - Prob. 38ECh. 8.4 - Prob. 39ECh. 8.4 - Prob. 40ECh. 8.4 - Prob. 41ECh. 8.4 - Prob. 42ECh. 8.4 - Prob. 43ECh. 8.4 - Prob. 44ECh. 8.4 - Prob. 45ECh. 8.4 - Prob. 46ECh. 8.4 - Prob. 47ECh. 8.4 - Prob. 48ECh. 8.4 - Prob. 49ECh. 8.4 - Prob. 50ECh. 8.4 - Prob. 51ECh. 8.4 - Evaluate the integrals in Exercises 39–54.
52.
Ch. 8.4 - Prob. 53ECh. 8.4 - Prob. 54ECh. 8.4 - Prob. 55ECh. 8.4 - Prob. 56ECh. 8.4 - Prob. 57ECh. 8.4 - Prob. 58ECh. 8.4 - Prob. 59ECh. 8.4 - Prob. 60ECh. 8.4 - Prob. 61ECh. 8.4 - Prob. 62ECh. 8.4 - Prob. 63ECh. 8.4 - Prob. 64ECh. 8.4 - Prob. 65ECh. 8.4 - Prob. 66ECh. 8.4 - Prob. 67ECh. 8.4 - Prob. 68ECh. 8.4 - Prob. 69ECh. 8.4 - Prob. 70ECh. 8.4 - Prob. 71ECh. 8.4 - Prob. 72ECh. 8.4 - Prob. 73ECh. 8.4 - Prob. 74ECh. 8.4 - Prob. 75ECh. 8.4 - Prob. 76ECh. 8.4 - Prob. 77ECh. 8.4 - Prob. 78ECh. 8.5 - Use the table of integrals at the back of the text...Ch. 8.5 - Prob. 2ECh. 8.5 - Prob. 3ECh. 8.5 - Prob. 4ECh. 8.5 - Prob. 5ECh. 8.5 - Prob. 6ECh. 8.5 - Prob. 7ECh. 8.5 - Prob. 8ECh. 8.5 - Prob. 9ECh. 8.5 - Prob. 10ECh. 8.5 - Prob. 11ECh. 8.5 - Prob. 12ECh. 8.5 - Prob. 13ECh. 8.5 - Prob. 14ECh. 8.5 - Prob. 15ECh. 8.5 - Prob. 16ECh. 8.5 - Prob. 17ECh. 8.5 - Prob. 18ECh. 8.5 - Prob. 19ECh. 8.5 - Prob. 20ECh. 8.5 - Prob. 21ECh. 8.5 - Prob. 22ECh. 8.5 - Prob. 23ECh. 8.5 - Prob. 24ECh. 8.5 - Prob. 25ECh. 8.5 - Prob. 26ECh. 8.5 - Prob. 27ECh. 8.5 - Prob. 28ECh. 8.5 - Prob. 29ECh. 8.5 - Prob. 30ECh. 8.5 - Prob. 31ECh. 8.5 - Prob. 32ECh. 8.5 - Prob. 33ECh. 8.5 - Prob. 34ECh. 8.5 - Prob. 35ECh. 8.5 - Prob. 36ECh. 8.5 - Prob. 37ECh. 8.5 - Prob. 38ECh. 8.5 - Prob. 39ECh. 8.5 - Prob. 40ECh. 8.5 - Prob. 41ECh. 8.5 - Prob. 42ECh. 8.5 - Prob. 43ECh. 8.5 - Prob. 44ECh. 8.5 - Use reduction formulas to evaluate the integrals...Ch. 8.5 - Prob. 46ECh. 8.5 - Prob. 47ECh. 8.5 - Prob. 48ECh. 8.5 - Prob. 49ECh. 8.5 - Prob. 50ECh. 8.5 - Prob. 51ECh. 8.5 - Prob. 52ECh. 8.5 - Prob. 53ECh. 8.5 - Prob. 54ECh. 8.5 - Prob. 55ECh. 8.5 - Prob. 56ECh. 8.5 - Prob. 57ECh. 8.5 - Prob. 58ECh. 8.5 - Prob. 59ECh. 8.5 - Prob. 60ECh. 8.5 - Prob. 61ECh. 8.5 - Prob. 62ECh. 8.5 - Prob. 63ECh. 8.5 - Prob. 64ECh. 8.6 - The instructions for the integrals in Exercises...Ch. 8.6 - Prob. 2ECh. 8.6 - Prob. 3ECh. 8.6 - Prob. 4ECh. 8.6 - The instructions for the integrals in Exercises...Ch. 8.6 - Prob. 6ECh. 8.6 - Prob. 7ECh. 8.6 - Prob. 8ECh. 8.6 - Prob. 9ECh. 8.6 - Prob. 10ECh. 8.6 - In Exercises 11–22, estimate the minimum number of...Ch. 8.6 - Prob. 12ECh. 8.6 - Prob. 13ECh. 8.6 - Prob. 14ECh. 8.6 - Prob. 15ECh. 8.6 - Prob. 16ECh. 8.6 - Prob. 17ECh. 8.6 - Prob. 18ECh. 8.6 - Prob. 19ECh. 8.6 - In Exercises 11–22, estimate the minimum number of...Ch. 8.6 - Prob. 21ECh. 8.6 - Prob. 22ECh. 8.6 - Prob. 23ECh. 8.6 - Prob. 24ECh. 8.6 - Prob. 25ECh. 8.6 - Prob. 26ECh. 8.6 - Prob. 27ECh. 8.6 - The error function The error function,
which is...Ch. 8.6 - Prob. 29ECh. 8.6 - Prob. 30ECh. 8.6 - Elliptic integrals The length of the...Ch. 8.6 - Prob. 32ECh. 8.6 - Prob. 33ECh. 8.6 - Prob. 34ECh. 8.6 - Prob. 35ECh. 8.6 - Prob. 36ECh. 8.6 - Prob. 37ECh. 8.6 - Prob. 38ECh. 8.6 - Prob. 39ECh. 8.6 - Prob. 40ECh. 8.7 - The integrals in Exercises 1-34 converge. Evaluate...Ch. 8.7 - Prob. 2ECh. 8.7 - Prob. 3ECh. 8.7 - Prob. 4ECh. 8.7 - Prob. 5ECh. 8.7 - Prob. 6ECh. 8.7 - Prob. 7ECh. 8.7 - Prob. 8ECh. 8.7 - Prob. 9ECh. 8.7 - Prob. 10ECh. 8.7 - Prob. 11ECh. 8.7 - Prob. 12ECh. 8.7 - Prob. 13ECh. 8.7 - Prob. 14ECh. 8.7 - Prob. 15ECh. 8.7 - Prob. 16ECh. 8.7 - Prob. 17ECh. 8.7 - Prob. 18ECh. 8.7 - Prob. 19ECh. 8.7 - Prob. 20ECh. 8.7 - Prob. 21ECh. 8.7 - Prob. 22ECh. 8.7 - Prob. 23ECh. 8.7 - Prob. 24ECh. 8.7 - Prob. 25ECh. 8.7 - Prob. 26ECh. 8.7 - Prob. 27ECh. 8.7 - Prob. 28ECh. 8.7 - Prob. 29ECh. 8.7 - The integrals in Exercises 1-34 converge. Evaluate...Ch. 8.7 - Prob. 31ECh. 8.7 - Prob. 32ECh. 8.7 - Prob. 33ECh. 8.7 - Prob. 34ECh. 8.7 - In Exercises 35–68, use integration, the Direct...Ch. 8.7 - Prob. 36ECh. 8.7 - Prob. 37ECh. 8.7 - Prob. 38ECh. 8.7 - Prob. 39ECh. 8.7 - Prob. 40ECh. 8.7 - Prob. 41ECh. 8.7 - Prob. 42ECh. 8.7 - Prob. 43ECh. 8.7 - Prob. 44ECh. 8.7 - Prob. 45ECh. 8.7 - Prob. 46ECh. 8.7 - Prob. 47ECh. 8.7 - Prob. 48ECh. 8.7 - Prob. 49ECh. 8.7 - Prob. 50ECh. 8.7 - Prob. 51ECh. 8.7 - Prob. 52ECh. 8.7 - Prob. 53ECh. 8.7 - Prob. 54ECh. 8.7 - Prob. 55ECh. 8.7 - Prob. 56ECh. 8.7 - Prob. 57ECh. 8.7 - Prob. 58ECh. 8.7 - Prob. 59ECh. 8.7 - In Exercises 35–68, use integration, the Direct...Ch. 8.7 - Prob. 61ECh. 8.7 - Prob. 62ECh. 8.7 - Prob. 63ECh. 8.7 - Prob. 64ECh. 8.7 - Prob. 65ECh. 8.7 - Prob. 66ECh. 8.7 - Prob. 67ECh. 8.7 - Prob. 68ECh. 8.7 - Prob. 69ECh. 8.7 - Prob. 70ECh. 8.7 - Prob. 71ECh. 8.7 - Prob. 72ECh. 8.7 - Prob. 73ECh. 8.7 - Prob. 74ECh. 8.7 - Prob. 75ECh. 8.7 - Prob. 76ECh. 8.7 - Prob. 77ECh. 8.7 - Prob. 78ECh. 8.7 - Prob. 79ECh. 8.7 - Prob. 80ECh. 8.7 - Prob. 81ECh. 8.7 - Prob. 82ECh. 8.7 - Prob. 83ECh. 8.7 - Prob. 84ECh. 8.7 - Prob. 85ECh. 8.7 - Prob. 86ECh. 8 - Prob. 1GYRCh. 8 - Prob. 2GYRCh. 8 - Prob. 3GYRCh. 8 - Prob. 4GYRCh. 8 - Prob. 5GYRCh. 8 - Prob. 6GYRCh. 8 - Prob. 7GYRCh. 8 - Prob. 8GYRCh. 8 - Prob. 9GYRCh. 8 - Prob. 10GYRCh. 8 - Prob. 11GYRCh. 8 - Prob. 12GYRCh. 8 - Prob. 13GYRCh. 8 - Prob. 1PECh. 8 - Prob. 2PECh. 8 - Prob. 3PECh. 8 - Prob. 4PECh. 8 - Prob. 5PECh. 8 - Prob. 6PECh. 8 - Prob. 7PECh. 8 - Prob. 8PECh. 8 - Prob. 9PECh. 8 - Prob. 10PECh. 8 - Prob. 11PECh. 8 - Prob. 12PECh. 8 - Prob. 13PECh. 8 - Prob. 14PECh. 8 - Prob. 15PECh. 8 - Prob. 16PECh. 8 - Prob. 17PECh. 8 - Prob. 18PECh. 8 - Prob. 19PECh. 8 - Prob. 20PECh. 8 - Prob. 21PECh. 8 - Prob. 22PECh. 8 - Prob. 23PECh. 8 - Prob. 24PECh. 8 - Prob. 25PECh. 8 - Prob. 26PECh. 8 - Prob. 27PECh. 8 - Prob. 28PECh. 8 - Prob. 29PECh. 8 - Prob. 30PECh. 8 - Prob. 31PECh. 8 - Prob. 32PECh. 8 - Prob. 33PECh. 8 - Prob. 34PECh. 8 - Prob. 35PECh. 8 - Prob. 36PECh. 8 - Prob. 37PECh. 8 - Prob. 38PECh. 8 - Prob. 39PECh. 8 - Prob. 40PECh. 8 - Prob. 41PECh. 8 - Prob. 42PECh. 8 - Prob. 43PECh. 8 - Prob. 44PECh. 8 - Prob. 45PECh. 8 - Prob. 46PECh. 8 - Prob. 47PECh. 8 - Prob. 48PECh. 8 - Prob. 49PECh. 8 - Prob. 50PECh. 8 - Prob. 51PECh. 8 - Prob. 52PECh. 8 - Prob. 53PECh. 8 - Prob. 54PECh. 8 - Prob. 55PECh. 8 - Prob. 56PECh. 8 - Prob. 57PECh. 8 - Prob. 58PECh. 8 - Prob. 59PECh. 8 - Prob. 60PECh. 8 - Prob. 61PECh. 8 - Prob. 62PECh. 8 - Prob. 63PECh. 8 - Prob. 64PECh. 8 - Prob. 65PECh. 8 - Prob. 66PECh. 8 - Prob. 67PECh. 8 - Prob. 68PECh. 8 - Prob. 69PECh. 8 - Prob. 70PECh. 8 - Prob. 71PECh. 8 - Prob. 72PECh. 8 - Prob. 73PECh. 8 - Prob. 74PECh. 8 - Prob. 75PECh. 8 - Prob. 76PECh. 8 - Prob. 77PECh. 8 - Prob. 78PECh. 8 - Prob. 79PECh. 8 - Prob. 80PECh. 8 - Prob. 81PECh. 8 - Prob. 82PECh. 8 - Prob. 83PECh. 8 - Prob. 84PECh. 8 - Prob. 85PECh. 8 - Prob. 86PECh. 8 - Prob. 87PECh. 8 - Prob. 88PECh. 8 - Prob. 89PECh. 8 - Prob. 90PECh. 8 - Prob. 91PECh. 8 - Prob. 92PECh. 8 - Prob. 93PECh. 8 - Prob. 94PECh. 8 - Prob. 95PECh. 8 - Prob. 96PECh. 8 - Prob. 97PECh. 8 - Prob. 98PECh. 8 - Prob. 99PECh. 8 - Prob. 100PECh. 8 - Prob. 101PECh. 8 - Prob. 102PECh. 8 - Prob. 103PECh. 8 - Prob. 104PECh. 8 - Prob. 105PECh. 8 - Prob. 106PECh. 8 - Prob. 107PECh. 8 - Prob. 108PECh. 8 - Prob. 109PECh. 8 - Prob. 110PECh. 8 - Prob. 111PECh. 8 - Prob. 112PECh. 8 - Prob. 113PECh. 8 - Prob. 114PECh. 8 - Prob. 115PECh. 8 - Prob. 116PECh. 8 - Prob. 117PECh. 8 - Prob. 118PECh. 8 - Prob. 119PECh. 8 - Prob. 120PECh. 8 - Prob. 121PECh. 8 - Prob. 122PECh. 8 - Prob. 123PECh. 8 - Prob. 124PECh. 8 - Prob. 125PECh. 8 - Prob. 126PECh. 8 - Prob. 127PECh. 8 - Prob. 128PECh. 8 - Prob. 129PECh. 8 - Prob. 130PECh. 8 - Prob. 131PECh. 8 - Prob. 132PECh. 8 - Prob. 133PECh. 8 - Prob. 134PECh. 8 - Prob. 135PECh. 8 - Prob. 1AAECh. 8 - Prob. 2AAECh. 8 - Prob. 3AAECh. 8 - Prob. 4AAECh. 8 - Prob. 5AAECh. 8 - Prob. 6AAECh. 8 - Prob. 7AAECh. 8 - Prob. 8AAECh. 8 - Prob. 9AAECh. 8 - Prob. 10AAECh. 8 - Prob. 11AAECh. 8 - Prob. 12AAECh. 8 - Prob. 13AAECh. 8 - Prob. 14AAECh. 8 - Prob. 15AAECh. 8 - Prob. 16AAECh. 8 - Prob. 17AAECh. 8 - Prob. 18AAECh. 8 - Prob. 19AAECh. 8 - Prob. 20AAECh. 8 - Prob. 21AAECh. 8 - Prob. 22AAECh. 8 - Prob. 23AAECh. 8 - Prob. 24AAECh. 8 - Prob. 25AAECh. 8 - Prob. 26AAECh. 8 - Prob. 27AAECh. 8 - Prob. 28AAECh. 8 - Prob. 29AAECh. 8 - Prob. 30AAECh. 8 - Prob. 31AAECh. 8 - Prob. 32AAECh. 8 - Prob. 33AAECh. 8 - Prob. 34AAE
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