- Chapter 1.1: Sets and Functions
- Chapter 1.2: Mathematical Induction
- Chapter 1.3: Finite and Infinite Sets
- Chapter 10.1: Definition and Main Properties
- Chapter 10.2: Improper and Lebesgue Integrals
- Chapter 10.3: Infinite Intervals
- Chapter 10.4: Convergence Theorems
- Chapter 11.1: Open and Closed Sets in IR
- Chapter 11.2: Compact Sets
- Chapter 11.3: Continuous Functions
- Chapter 11.4: Metric Spaces
- Chapter 2.1: The Algebraic and Order Properties of IR
- Chapter 2.2: Absolute Value and the Real Line
- Chapter 2.3: The Completeness Property of R
- Chapter 2.4: Applications of the Supremum Property
- Chapter 2.5: Intervals
- Chapter 3.1: Sequences and Their Limits
- Chapter 3.2: Limit Theorems
- Chapter 3.3: MonotoneSequences
- Chapter 3.4: Subsequences and the Bolzano- Weierstrass Theorem
- Chapter 3.5: The Cauchy Criterion
- Chapter 3.6: Properly Divergent Sequences
- Chapter 3.7: Introduction to Infinite Series
- Chapter 4.1: Limits of Functions
- Chapter 4.2: 4.2 Limit Theorems
- Chapter 4.3: Some Extensions of the Limit Conceptt
- Chapter 5.1: Continuous Functions
- Chapter 5.2: Combinations of Continuous Functions
- Chapter 5.3: Continuous Functions on Intervals
- Chapter 5.4: Uniform Continuity
- Chapter 5.5: Continuity and Gauges
- Chapter 5.6: Monotone and Inverse Functions
- Chapter 6.1: The Derivative
- Chapter 6.2: The Mean Value Theorem
- Chapter 6.3: L'Hospital's Rules
- Chapter 6.4: Taylor's Theorem
- Chapter 7.1: Riemann Integral
- Chapter 7.2: Riemann Integrable Functions
- Chapter 7.3: The Fundamental Theorem
- Chapter 7.4: Approximate Integration
- Chapter 8.1: Pointwise and Uniform Convergence
- Chapter 8.2: Interchange of Limits
- Chapter 8.3: The Exponential and Logarithmic Functions
- Chapter 8.4: The Trigonometric Functions
- Chapter 9.1: Absolute Convergence
- Chapter 9.2: Tests for Absolute Convergence
- Chapter 9.3: Tests for Nonabsolute Convergence
- Chapter 9.4: Series of Functions
Introduction to Real Analysis 3rd Edition - Solutions by Chapter
Full solutions for Introduction to Real Analysis | 3rd Edition
ISBN: 9780471321484
Introduction to Real Analysis | 3rd Edition - Solutions by Chapter
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Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. The full step-by-step solution to problem in Introduction to Real Analysis were answered by , our top Calculus solution expert on 03/14/18, 07:51PM. This expansive textbook survival guide covers the following chapters: 48. Since problems from 48 chapters in Introduction to Real Analysis have been answered, more than 3219 students have viewed full step-by-step answer. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3.
Key Calculus Terms and definitions covered in this textbook
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Bounded
A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.
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Closed interval
An interval that includes its endpoints
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Compounded k times per year
Interest compounded using the formula A = Pa1 + rkbkt where k = 1 is compounded annually, k = 4 is compounded quarterly k = 12 is compounded monthly, etc.
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Direction vector for a line
A vector in the direction of a line in three-dimensional space
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equation of a hyperbola
(x - h)2 a2 - (y - k)2 b2 = 1 or (y - k)2 a2 - (x - h)2 b2 = 1
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Inverse cosine function
The function y = cos-1 x
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Inverse reflection principle
If the graph of a relation is reflected across the line y = x , the graph of the inverse relation results.
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Multiplication principle of probability
If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(A|B) # P(B)
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Negative angle
Angle generated by clockwise rotation.
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Opposite
See Additive inverse of a real number and Additive inverse of a complex number.
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Paraboloid of revolution
A surface generated by rotating a parabola about its line of symmetry.
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Partial fraction decomposition
See Partial fractions.
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Permutations of n objects taken r at a time
There are nPr = n!1n - r2! such permutations
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Positive linear correlation
See Linear correlation.
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Power function
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.
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Sample standard deviation
The standard deviation computed using only a sample of the entire population.
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Third quartile
See Quartile.
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Unit vector
Vector of length 1.
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Variance
The square of the standard deviation.
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xy-plane
The points x, y, 0 in Cartesian space.