Explanation Theorem used: The Integral Test : Suppose that f is a continuous, positive, and decreasing function on [ 1 , ∞ ] . If f ( n ) = a n for all n ≥ 1 , then ∑ n − 1 ∞ a n and ∫ 1 ∞ f ( x ) d x either both converge or both diverge. The given function is ∫ 1 ∞ 2 ( x 2 + 1 ) 1.1 d x . Here, the function is f ( x ) = 2 ( x 2 + 1 ) 1.1 . Since f is continuous, positive, and decreasing on [ 1 , ∞ ] , use Integral test to evaluate ∫ 1 ∞ f ( x ) d x as follows. lim b → ∞ ∫ 1 b 2 ( x 2 + 1 ) 1.1 d x = 2 lim b → ∞ ∫ ( x 2 + 1 ) − 1.1 + 1 − 1.1 + 1 d x = − 2 0.1 lim b → ∞ [ 1 ( x 2 + 1 ) 0.1 ] 1 b = − 20 lim b → ∞ [ 1 ( b 2 + 1 ) 0

Applied Calculus for the Managerial, Life, and Social Sciences

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ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Chapter 11.4, Problem 58E

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Whether the statement “If ∫1∞2(x2+1)1.1dx converges” is true or false; explain if it is true, or give an example if it is false.

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Chapter 11.4, Problem 57E

Chapter 11.4, Problem 59E

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3. Suppose that A is 5 x 5 and rank(A)=4. Use this information to answer the following. a. Give a geometric description of nullspace(A). Justify. b. Is A invertible? Justify. c. Give a geometric description of the span of the column vectors of A. What space are the column vectors of A in? Justify. d. What is determinant of A? Justify.

2. Consider the matrix: A || 1 1 -3 14 2 1 01 4 1 2 2 -26 1 -3 1 5] a) What is rank(A)? b) Is A invertible? Justify. c) Find the nullspace(A). Justify. d) Is the trivial solution the only solution to Ax=0? Justify. e) What is the span of the column vectors of A? Justify.

E 5. Suppose that S={v € R²: v = [2x² - 3]}. Is S a subspace of R²? Prove or disprove

Chapter 11 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

Ch. 11.1 - Prob. 1CQ Ch. 11.1 - Prob. 2CQ Ch. 11.1 - Prob. 1E Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E

Ch. 11.1 - In Exercises 110, find the first three Taylor...Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - In Exercises 1120, find the nth Taylor polynomial...Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Let f(x) = ex. a. 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Whether the statement “If ∫ 1 ∞ 2 ( x 2 + 1 ) 1.1 d x converges” is true or false; explain if it is true, or give an example if it is false.

Solution Summary: The author explains whether the statement "If displaystyle 'underset'' converges" is true or false.

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Whether the statement “If ∫1∞2(x2+1)1.1dx converges” is true or false; explain if it is true, or give an example if it is false.

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Chapter 11 Solutions