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Solutions for Chapter 11.2: Compact Sets

Full solutions for Introduction to Real Analysis | 3rd Edition

ISBN: 9780471321484

Solutions for Chapter 11.2: Compact Sets

This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Introduction to Real Analysis, edition: 3. Introduction to Real Analysis was written by and is associated to the ISBN: 9780471321484. Since 15 problems in chapter 11.2: Compact Sets have been answered, more than 9591 students have viewed full step-by-step solutions from this chapter. Chapter 11.2: Compact Sets includes 15 full step-by-step solutions.

Key Calculus Terms and definitions covered in this textbook
  • Blind experiment

    An experiment in which subjects do not know if they have been given an active treatment or a placebo

  • Directed distance

    See Polar coordinates.

  • Factor

    In algebra, a quantity being multiplied in a product. In statistics, a potential explanatory variable under study in an experiment, .

  • Finite sequence

    A function whose domain is the first n positive integers for some fixed integer n.

  • Graph of an inequality in x and y

    The set of all points in the coordinate plane corresponding to the solutions x, y of the inequality.

  • Histogram

    A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.

  • Inductive step

    See Mathematical induction.

  • Multiplicative identity for matrices

    See Identity matrix

  • Normal distribution

    A distribution of data shaped like the normal curve.

  • One-to-one rule of exponents

    x = y if and only if bx = by.

  • Parameter

    See Parametric equations.

  • Polynomial in x

    An expression that can be written in the form an x n + an-1x n-1 + Á + a1x + a0, where n is a nonnegative integer, the coefficients are real numbers, and an ? 0. The degree of the polynomial is n, the leading coefficient is an, the leading term is anxn, and the constant term is a0. (The number 0 is the zero polynomial)

  • Probability function

    A function P that assigns a real number to each outcome O in a sample space satisfying: 0 … P1O2 … 1, P12 = 0, and the sum of the probabilities of all outcomes is 1.

  • Pythagorean

    Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

  • Range of a function

    The set of all output values corresponding to elements in the domain.

  • Residual

    The difference y1 - (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.

  • Rose curve

    A graph of a polar equation or r = a cos nu.

  • Slope-intercept form (of a line)

    y = mx + b

  • x-axis

    Usually the horizontal coordinate line in a Cartesian coordinate system with positive direction to the right,.

  • Yscl

    The scale of the tick marks on the y-axis in a viewing window.

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