Problems 39–66 are mixed—some may require use of the integration -by-parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula. Assume that g ( x ) > 0 whenever ln g ( x ) is involved. 46. ∫ 0 2 ln ( 4 − x ) d x
Problems 39–66 are mixed—some may require use of the integration -by-parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula. Assume that g ( x ) > 0 whenever ln g ( x ) is involved. 46. ∫ 0 2 ln ( 4 − x ) d x
Solution Summary: The author explains how the value of integral displaystyle is 2.158.
Problems 39–66 are mixed—some may require use of the integration-by-parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula. Assume that g (x) > 0 whenever ln g(x) is involved.
46.
∫
0
2
ln
(
4
−
x
)
d
x
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Consider the graph/network plotted below.
1
6
5
3
Explicitly give (i.e., write down all of the entries) the adjacency matrix A of the graph.
. Given the function f: XY (with X and Y as above) defined as
f(2) = 2, f(4) = 1,
ƒ(6)=3, ƒ(8) = 2,
answer the following questions. Justify your answers.
(a) [4 points] Is f injective?
(b) [4 points] Is f surjective?
(c) [2 points] Is f bijective?
1. Let
15 -14
A
= -10
9
13-12
-8 7
11
15
-14 13 -12
-6 and B =
-10 9 -8 7 -6
5
-4
3 -2
E
5 -4 3 -2 1
Explicitly give the values of A2,3, A1,5, and B1,4-
Is A a 5 x 3 matrix? Explain your answer.
Are A and B (mathematically) equal? Explain your answer.
Chapter 6 Solutions
MyLab Math with Pearson eText - Stand Alone Access Card - for Calculus for Business, Economics, Life Sciences & Social Sciences, Brief Version (14th Edition)
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