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Math
CalculusMultivariable Calculus8th Edition

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Chapter 11.4, Problem 41E
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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
BuyFindarrow_forward

Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

  1. (a) Suppose that Σ an and Σ bn are series with positive terms and Σ bn is divergent. Prove that if

lim n → ∞ a n b n = ∞

then Σ an is also divergent.

  1. (b) Use part (a) to show that the series diverges.
    1. (i) ∑ n = 2 ∞ 1 ln n
    2. (ii) ∑ n = 1 ∞ ln n n

(a)

To determine

To prove: The series ∑an is divergent.

Explanation

Result used:

“Suppose that ∑an and ∑bn are the series with positive terms,

(a) If ∑bn is convergent and an≤bn for all n , then ∑an is also convergent.

(b) If ∑bn is divergent and an≥bn for all n , then ∑an is also divergent.”

Given:

The series ∑an and ∑bn is divergent, limn→∞anbn=∞ . (1)

Proof:

Consider the series ∑an and ∑bn

(b) (i)

To determine

To show: The series ∑n=1∞1lnn diverges.

(ii)

To determine

To show: The series ∑n=1∞lnnn diverges.

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Chapter 11.4,
Problem 40E
Chapter 11.4,
Problem 42E
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Prove the identity. 16. cosh 2x = cosh2x + sinh2x

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Numerical Integration (a) Write an integral that represents the area of the region in the figure. (b) Use the M...

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Finding a Particular Solution Using Separation of Variables In Exercises 39-42, find the particular solution of...

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a. Factor x as a product of two polynomials of degree 1 in Z12[ x ]. b. Factor x as a product of two polynomial...

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Find , 0o360o, given the following information. tan=1 with in QIII

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Rewritten in reverse order,

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For f(x)=x2+x, we may write f (x) = (h g)(x), where: a) h(x)=x and g(x) = x2 + x b) h(x) = x2 + x and g(x)=x c...

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SELF-STORAGE UNITS As part of its expansion plan, LA Self Storage is planning to construct a facility comprisin...

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In a small city, approximately 15% of those eligible are called for jury duty in any one calendar year. People ...

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Write two-column proofs for Review Exercises 39 to 46. Given: KFFH Prove: KFJ is complementary to JFH

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Midpoint Rule In Exercises 127 and 128, use the Midpoint Rule with n=12 to approximate the value of the definit...

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Writing a Tangent PlaneIn Exercises 57 and 58, show that the tangent plane to the quadric at the point (x0,y0,z...

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Finding the Standard Equation of a Hyperbola In Exercises 21-24, find the standard form of the equation of the ...

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The cost of consumer purchases such as single-family housing, gasoline, Internet services, tax preparation, and...

Statistics for Business & Economics, Revised (MindTap Course List)

Subtract the following expressions as indicated. (xy2x2y2+x2y2)0

Mathematics For Machine Technology

Perform the operations and simplify. 6x3+x2-xx+23x2-xx2+4x+4

College Algebra (MindTap Course List)

Public transportation and the automobile are two methods an employee can use to get to work each day. Samples o...

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Mueller and Oppenheimer (2014) conducted a series of studies comparing the effectiveness of taking classroom no...

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Describe the basic concern with measuring inter-rater reliability and explain how Cohens kappa addresses this c...

Research Methods for the Behavioral Sciences (MindTap Course List)

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