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Numerical Series Expansion

Mathematicians, scientists, and engineers often need solutions for difficult to unsolvable equations in order to progress in their work. Fortunately, through various methods of numerical and polynomial series expansions, some of the most problematic equations can be approximated to easily workable forms. Please post all questions regarding the various expansions and series, such as the Taylor and Maclaurin series expansions, the binomial expansion, and the geometric expansion, as well as the rules that govern them, into this category.

468 Questions

What is meant by Cauchy's constants?

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Cauchy's constants refer to a set of constants used in the theory of elasticity to describe the stress-strain relation in a material. These constants are determined based on the material properties and define how the material responds to deformation under stress. They are used in the Cauchy stress tensor to represent the stress state at a point in a material.

What is the formula for exponential growth?

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It can vary , but it is something along the lines of

G(t) = Ae^(xt)

Where

'G' is growth at time 't'

'A' is a constnt

'e' is the exponential 2.7818....

'x' is the variable factor

't' is the time.

e^(xt) is the exponential raised to the power of 'variable factor multiplied to time'.

What is a example of convergence?

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An example of convergence is when a group of friends with differing opinions gradually come to a consensus on where to go for dinner by considering everyone's preferences and finding a common choice that satisfies all parties.

What is the relationship between natural frequencies of an object and the harmonics that can be created in the object?

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The natural frequencies of an object are the frequencies at which the object tends to vibrate easily. Harmonics are frequencies that are integer multiples of the fundamental frequency. When an object is excited at its natural frequencies, it tends to resonate and produce harmonics of those frequencies.

A force of 1.2 kN equals?

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1.2 kN is equivalent to 1200 N (Newtons).

Why to use a converging and diverging nozzle in a steamturbine?

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Converging nozzles are used to accelerate steam flow by converting pressure energy into kinetic energy, while diverging nozzles help to convert this kinetic energy back into pressure energy, resulting in increased efficiency and power output for the steam turbine. This design allows for optimal steam expansion and energy conversion in the turbine.

What is ungrouped data in statistics?

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Ungrouped data in statistics refers to raw, individual data points that have not been sorted or organized into any specific groups or categories. This type of data is often presented in a list format and may require further analysis or manipulation to draw meaningful insights or conclusions.

Sample of a very short story-plot summary?

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A young girl discovers a mysterious portal in her backyard that leads to a magical kingdom. She embarks on a journey to rescue the kingdom from an evil sorcerer, learning about courage and friendship along the way. In the end, she unlocks her true potential and saves the kingdom from destruction.

Why was there no 1994 World Series?

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The 1994 World Series was canceled due to a players' strike that began on August 12, 1994, and led to the remainder of the season being canceled, including the World Series. This was the first time in 90 years that the World Series was not played.

What is the objective for numerical maths?

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The objective is to provide approximate solutions for problems that don't have a traditional (exact) solution. For example, numerical integration can provide definite integrals in cases where you can't find an exact solution via an antiderivative. Note that in this example, you can get the answer as exact as you want - that is, you can make the error as small as you want (but not zero).

What is the pattern 1-5-1-15-45-1?

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One possible answer is:

Un = (-3n5 + 38n4 - 159n3 + 250n2 - 90n - 30)/6

Why you use series expansion ie Taylor or maclaron or any other series during solving problems?

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Some functions cannot be evaluated by normal means and you need an infinite series to get approximate answers.

What does an binomial expansion do?

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Binomial Expansion makes it easier to solve an equation. It brings an equation of something raised to a power down to a solveable equation without parentheses.

How do you tell if a geometric series diverges or con verges?

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If the absolute value of the common multiple is less than 1 then it converges and, if not, it diverges.

How do you do sums?

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The answer will depend on what kind of sums.

How do you get numbers 8 9 and 12 by using four 5's?

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The answer depends on what mathematical operations are permitted.

One set of solutions is:


8 = 5!/(5+5+5)

9 = 5 + 5 - 5/5

12 = .5*5!/sqrt(5*5)

Write 12.579 in word form?

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Twelve and five hundred seventy-nine thousandths.

How many pounds are equal to 1362grams?

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1362 grams = 3.00 pounds.