41 Answered Questions for the topic Analysis

Analysis Proofs Sets Index

06/06/18

How do I prove that a set of closed sets is itself closed.

Hi, I have been asked the following but am struggling.   Let {Ωa : a ∈ I} be an arbitrary family of closed sets Ωa ⊆ Rd with an index set I. Prove that   ∩     Ωa a ∈ I   is a closed... more
Analysis Limits Matrices

02/21/18

Tough analysis related question - please help!

Let A= a b           c  d   be an arbitrary 2x2 matrix. Let xn ⊆ R2 and suppose that (xn)→x for some x∈R2. Prove that (Axn)→Ax

Show that the set GL(n, R) of invertible n × n real matrices is open in the space of n × n matrices (metric spaces, Real analysis)

Show that the set GL(n, R) of invertible n × n real matrices is open in the space of n × n matrices, with the metric being the Euclidean metric in Rn^2 when a matrix is identified with a long, n2... more

01/14/18

Limits of sequences and series

How do I go about proving limits for given sequences and series, for example how would i prove that the limit when x tends to infinity of n^(1/n)=1?

Can someone help me prove the below by induction please? Thanks :)

Prove by induction:nΣ(q^i) = (q^(n+1)-1)/(q-1)i=0

11/28/17

How would I define a bounded series?

Please note that I am talking about a series and NOT  a sequence
Analysis Math Proofs

11/07/17

The question is about proving limits

a) Show that if xn≠0, where n(∈) is a subset of N then lim(xn)=0 if and only if lim(1/xn2)=infinity    b) Give an example for which lim(xn)=0 but lim(1/x2n) does not exist  
Analysis Limits Sequences

10/01/17

Let {xn} be a bounded sequence such that any of its convergent proper subsequences converge to the same limit l. Prove that {xn} converges to l.

Any hints on how to prove this? What can we use a a proper subsequence, knowing that a proper subsequence is any subsequence except for the sequence it self. 
Analysis

09/06/17

Henry had to turn up/off/down the offer to work abroad for family reasins?

for my assignment aahh

I want to know if this can be proved that it is true.

I suppose we know that x > 0 . m is an integer and w is real number , where x = (1 + w)m  ,0<=w<=0.5
Analysis

04/15/16

How many of each animal exists in each population initially?

A rabbit population is modeled by R(t)=3 to the (t) power+5 and a turtle population is modeled by L(t)=10t+6 for (t) > 0  
Analysis

02/09/16

Carter and Ari had 240 altogether. Ari had twice as much as Carter after Carter gave him 16. How much more money did Ari have than Carter in the beginning?

Carter and Ari had 240 altogether. Ari had twice as much as Carter after Carter gave him 16. How much more money did Ari have than Carter in the beginning?

10/11/15

Lord of the Flies - Piggy quotes and analysis

Hi, I'm looking for quotes that best show Piggy's character traits in Lord of the Flies. A short analysis of the quotes would be useful too.   Thank you! :)

09/30/15

statistics help

The number of fatal car crashes per day in Houston is shown in the table below. Let X be the random variable representing the number of fatal crashes. Find P(X < 2). Hint: convert the table to a... more

03/24/15

Finding an irrational function with 2 horizontal asymptotes y=1 and y=5.

I can't seem to find an irrational function with the 2 horizontal asymptotes y=1 and y=5.I've looked everywhere and tried all I know, I keep getting 2 asymptotes that the contrary of each other eg.... more
Analysis

03/15/15

Solving the Net present Value

A popular movie actress has been offered a two-year contract. She can either accept $2,350,000 now or accept monthly amounts of $100000 payable at the end of each month. If money can be invested at... more
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