13 Answered Questions for the topic Real Analysis

#### Power Series Representation of a Function

Find a power series representation for the following functions and determine the interval ofconvergence and radius of convergence.f(x) = 6x/(5x2 - 4x - 1)

#### Limit of a Sequence- Epsilon Delta Definition

Let an be a sequence of real numbers such that lim n-->infinity (an)=3.By directly using the definition of the limit of a sequence, show that lim n-->infinity(2an/(2an+3))=2

04/08/20

#### Evaluating the following limit

Evaluate the following limit: limn→∞{(4n-C(2n+1,n))/(4n)} Where C(a,b) = a!/(a-b)!b!Hint: Use asymptotics to bound the limit and then make use of the squeeze theorem.Spoiler: The answer is 1.

#### Prove that T is a linear operator

Let T:R2→R2 be the function defined by T(〈x,y〉) = 〈-y,x〉.Hint: We want to show T(u + v) = T(u) + T(v) and T(λu) = λT(u) For all u,v ∈ R2 and λ ∈ R.

02/23/20

#### Supremum and infimum

X1 = { x | x = 0 or x = (1/n) ; n € N(N - set of natural numbers)Find the supremum and infimum(if they exists ) of set X1

05/16/19

#### Using Riemann Integral for proof.

Prove that f(x) = absolute value of x when x is not 0 and f(0)=9on the closed interval [-1, 1] is integrable .

#### Mathematics GRE subject test Prerequisites?

I looked at the Mathematics GRE subject test's website and it says the material covered is 50 % Calculus, 25 % Algebra, 25 % Additional Topics. I have taken two semesters of real analysis, abstract...
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#### What kind of "mathematical object" are limits?

When learning mathematics I tend to try to reduce all the concepts I come across to some matter of interaction between sets and functions (or if necessary the more general Relation) on them....
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03/22/19

#### Geometrical Interpretation of Cauchy Riemann equations?

Differentiation has an obvious geometric interpretation, and the Cauchy Riemann equations are closely linked with differentiation.
Do the Cauchy Riemann equations have a geometric interpretation?

03/22/19

#### What are the main uses of Convex Functions?

Up till now I have just learned that the concept of convexity in functions of one variable is used to complete the graphs of functions, meaning to locate points of inflexion and see if the graph is...
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03/14/19

#### Who came up with the $\\varepsilon$-$\\delta$ definitions and the axioms in Real Analysis?

I've seen a lot of definitions of notions like boundary points, accumulation points, continuity, etc, and axioms for the set of the real numbers. But I have a hard time accepting these as "true"...
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Real Analysis

02/22/19

#### How to prove a solution exist between an interval.

For example f(x)= (5/x-1) +(7/x-2) has a solution between 1 and 2. I can see this graphically but do not know how to proof it mathematically

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