38 Answered Questions for the topic Analysis

08/10/20

#### Show that the solutions of the differential equation dy /dx = f (y) are monotonic functions.

#### Series Expansion of Cos(x) centered at x=0

Considering first six terms in the series expansion of cos x, calculate the approximatevalue of the cos x , centered at x=0.Discuss the types of errors are in this calculation.

#### What is the Syntax of this excerpt from The Crisis Speech by Carrie Chapman Catt? What was the goal of this Speech and how does the syntax in this excerpt help to achieve that goal?

"The object of the life of an organized movement is to secure its aim. Necessarily, it must obey the law of evolution and pass through the stages of agitation and education and finally through the...
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#### In "Al Capone Does my Shirts" by Gennifer Choldenko, is Piper's scheme corruption?

In the novel, Al Capone Does my Shirts by Gennifer Choldenko, is Piper's Scheme considered a type of corruption? Also, is Moose getting popularity also a type of corruption? If not, what other 3...
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11/19/19

#### Use paired or unpaired t-test?

I am doing an analysis on whether there is a meaningful difference between the temperature in June and December in Hawaii. I first identify the average temperature in June at all stations across...
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#### Vector Differentiation

Prove that (grad)^2 f(r) = D^2/dr^2 + (2/r) Df/DrWhere D^2/dr^2 refers to the second partial derivative of f , w.r.t. r and Df/ Dr refers to partial derivative of f, w.r.t rvector r = xi + yj + zk...
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06/27/19

#### Mathematical methods for analysing melodic contour?

Are there any mathematical methods for identifying melodic shape, identifying motifs and general pattern recognition?

06/22/19

#### If A minor doesn't have any accidentals, is it still minor?

As part of a music course, we have to compose a 3 minute long piece based on a river's journey. Having finished the composition, we now have to write a set of sleeve notes - basically an analysis...
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05/17/19

#### If A minor doesn't have any accidentals, is it still minor?

As part of a music course, we have to compose a 3 minute long piece based on a river's journey. Having finished the composition, we now have to write a set of sleeve notes - basically an analysis...
more

#### Why are dolls, teddy bears, etc. used as horror objects in horror films?

In many horror films, toys such as dolls, teddy bears, and puzzle boxes are used as objects which the spirits/ghosts use to scare people. Some examples would be Annabelle, the crooked man musical...
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04/27/19

#### How would one create music based on the principles of Cubism?

How would one create music based on the principles of Cubism?
(e.g., 20th century painters: Pablo Picasso, Georges Braque, Juan Gris, Fernand Léger)
The basic definition of Cubism calls for the...
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04/23/19

#### How to provide traditional upper management early analyses in an agile project?

I was discussing moving our process to become more agile with our (mostly traditional) Chief Information Officer (CIO).The CIO's stance was that >=80% of the requirements need to be defined (and...
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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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#### What is a simple example of a limit in the real world?

This morning, I read Wikipedia's informal definition of a limit:
> Informally, a function f assigns an output $f(x)$ to every input $x$. The
> function has a limit $L$ at an input $p$ if...
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03/14/19

#### What are the official modes from Ionian to Locrian?

I am having some confusion is respects to the formal definition of what the various modes are. I know that their defined in relation to their scale, however, I've come to realise this may not be...
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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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03/14/19

#### How would one create music based on the principles of Cubism?

How would one create music based on the principles of Cubism?(e.g., 20th century painters: Pablo Picasso, Georges Braque, Juan Gris, Fernand Léger)The basic definition of Cubism calls for the use...
more

03/13/19

#### Why do movie coroners eat while they do an autopsy?

I have seen this in movies and in TV. They are either already eating, un wrapping their lunch or offering food to the cop that wants info on the body. I would have though food within range of a...
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06/14/18

#### Proving continuity of a differentiable function

Hi I have been given a function f:(a,b)→R, which is differentiable on (a,b). How do I use this information to prove that f is also continuous on (a,b)? Thanks.

Analysis

06/11/18

#### What is the definition of a regulated function?

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06/10/18

#### Proving continuity of a differentiable function.

Hi
I have been given a function f:(a,b)→R, which is differentiable on (a,b). How do I use this information to prove that f is also continuous on (a,b)?
Thanks.

#### 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...
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#### 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...
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