23 Answered Questions for the topic Real Analysis

06/08/25

Monotone subsequence of an infinite sequence
Does every infinite sequence have a monotone subsequce? Here by "monotone" we may either (non-strictly) increasing or decreading. More precisely, given a sequence (an)n≥1, does there exist a... more
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Real Analysis

02/23/22

MATHEMATICS 3 question
Prove that there is a mapping from a set to itself that is one-to-one but not onto iff there is a mapping from the set to itself that is onto but not one-to-one. [Hint: You need to distinguish... more
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Real Analysis Calculus Sequences

10/28/21

Sequences (Calculus 3)
State whether the following statement is True or False. If True, state a relevant theorem from where it follows. if False, give a counter-example.If an and bn are any two sequences such that an +... more
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03/03/21

Use the sandwich lemma to solve --> xn := 1/ sqrt (n^ 2 +1) + 1 /sqrt (n^ 2 +2) +...+ 1 /sqrt (n^ 2 +n) converges to 1
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03/03/21

Use the sandwich lemma to solve --> Let 0<a<b . The sequence ((a^ n +b^ n )^ 1/n ) converges to b .
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Real Analysis Algebra 2 Continuity

01/31/21

Intermediate value theorem question
Hi, I need to show that there at least two values of x in the interal [0, pi] for which 3 sin x - 2 cos x = xI think i need to use the Intermediate value theorem, but not sure how i would do... more
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Real Analysis Math Calculus Maths

11/17/20

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)
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Real Analysis Math Calculus Maths

10/10/20

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
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Real Analysis

05/19/20

I must find sum of this functional serie. I don't know what to do here.
x+x2/2+x3/3+x4/4+...+xn/n and x∈(-1,1)
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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.
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Real Analysis Math Calculus Geometry

04/08/20

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.
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02/23/20

Sequences and supremum and infimum

Let X = { 1.6, 1.66 , 1.666 , 1.6666 , ........}Find supremum and infimum of X
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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
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Real Analysis

09/28/19

Proof related to Supremum and Infimum

S is setx belongs to real number RShow that Sup (S+x)= Sup S+ x
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09/09/19

Prove thisIf {sn} , n=1 to infinity is a sequence of real numbers and if lim(n tends to infinity)sn = M , where M is not equal to , then lim(n tends to infinity) 1/sn = 1/M
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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 .
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Real Analysis Calculus Gre Gre Exam

03/24/19

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... more
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Real Analysis Calculus Limits Functions

03/23/19

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.... more
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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?
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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... more
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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"... more
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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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Real Analysis

08/13/15

taylor's theorem: real analysis
state and proof taylor's theorem?  
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