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Real Analysis

Real Analysis refers to the study of real valued functions. It particularly focuses on the properties of these functions, including but not limited to, the convergence and limits of sequences of real numbers, as well as the calculus of real numbers. In dealing with Real Analysis, it is important to understand the different terms. If a limit for a particular sequence exists, then the sequence is called convergent; however if the limit for a particular sequence does not exist, then the sequence is called divergent.

For example, if the sequence was 1, ½, 1/3 , ¼, 1/5, 1/6 and so on, this can be written in the following form:



j is the denominator of the function

inf is infinity

This sequence eventually converges to zero, because as j approaches infinity, the denominator gets extremely large, leaving the output of the function to be extremely small. However, the important aspect to consider is that the series never actually reaches zero, but it can get as infinitesimally close to it. This is why the study of limits in this particular context is considered under Real Analysis.

Categories within Real Analysis


Postings: 1,061

A Derivative is a measure of how the output of a specific function, which is not limited to y or f(x), changes with respect to the input.


Postings: 1,949

An Integral is a function, F, which can be used to calculate the area bound by the graph of the derivative function, the x-axis, the vertical lines x=a and x=b.

Sequences Limit Consequences

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Limits, Differentiation 8 Questions

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Series of Logical Arguments - Cutting Emissions

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Taylor Series Calculus

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Sequences and Limits on Epsilon

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uniform convergence and proof

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Cost Accounting CVP Analysis and Price Changes

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Real Analysis Textbook Metric Spaces

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Series - ratio test

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Real Analysis Functions

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Lipschitz functions convergence

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Real numbers analysis

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Power series solution

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Statistics - 2.1 Calculate the most appropriate measures of central tendency for each variable listed. Show all work. Explain your choices in each case. Discuss what each result means in real terms. ... [See the attached questions file.]

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Series and Binomial Theorem

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Derivatives, Integrals, Limits and Convergence

Please see the attached file for the fully formatted problems. Question 1 Differentiate the function f(x) = (a) xlnx - x (b) x5lnx (c) (lnx)2 (d) 1-x ________________________________________lnx Question 2 Figure 2.1 ?(x) = ln ^/¯ (9-x2) ________________________________________(4+x2)

There are twelve problems involving functions, continuity, finding slope using predictor formula, tangent line to a curve, trajectory of a projectile, finding limits, finding limits using squeeze law and continuity of functions.

Please refer to the attached file to view the complete questions. ======================================== Question 1 Figure 1.1 y = f(x) = (2x+4)2 - (2x - 4)2 . Apply the slope predictor formula to find the slope of the line tangent to Figure 1.1. Then write the equation of the line tangent to the graph of f at