In calculus,

**Taylor's theorem**gives an approximation of a k-times differentiable function around a given point by a k-th order**Taylor**polynomial. The exact content of "**Taylor's theorem**" is not universally agreed upon.Besides, why do we use Taylor series?

It is a

**series**that is**used**to create an estimate (guess) of what a function looks like. There is also a special kind of**Taylor series**called a Maclaurin**series**. In mathematics, a**Taylor series**shows a function as the sum of an infinite**series**. The sum's terms are taken from the function's derivatives.What is the Taylor series for?

In mathematics, a

**Taylor series**is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point. A function can be approximated by using a finite number of terms of its**Taylor series**.1

## What is Taylor's theorem used for?

A

**Taylor series**is an idea**used in**computer science, calculus, and other kinds of higher-level mathematics. It is a**series**that is**used to**create an estimate (guess) of what a function looks like. There is also a special kind of**Taylor series**called a Maclaurin**series**.**Taylor series**come from**Taylor's theorem**.2

## Is a power series a Taylor series?

The 's may not have the form f ( n ) ( x 0 ) / n ! , so that not every

**power series is a Taylor series**(although every**Taylor series**is a**power series**). In this case, the coefficients are encoding information about some sequence of numbers , and we examine the**series**formally to gather information about this sequence.3

## What is Taylor's formula?

A one-dimensional

**Taylor**series is an expansion of a real function about a point is given by. (1) If , the expansion is known as a Maclaurin series.**Taylor's theorem**(actually discovered first by Gregory) states that any function satisfying certain conditions can be expressed as a**Taylor**series.4

## What is the Maclaurin series for?

A

**Maclaurin series**is a**Taylor series**expansion of a function about 0, (1)**Maclaurin series**are named after the Scottish mathematician Colin**Maclaurin**. The**Maclaurin series**of a function up to order may be found using**Series**[f, x, 0, n ].5

## What is the radius of convergence of the series?

**Radius of Convergence**. A power series will

**converge**only for certain values of . For instance, converges for . In general, there is always an interval in which a power series converges, and the number is called the

**radius of convergence**(while the interval itself is called the interval of

**convergence**).

6

## What is a constant example?

more A fixed value. In Algebra, a

**constant**is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number.**Example**: in "x + 5 = 9", 5 and 9 are constants. If it is not a**constant**it is called a variable.7

## What is the meaning of Leading term?

**Leading Term**. The

**term**in a polynomial which contains the highest power of the variable. For example, 5x

^{4}is the

**leading term**of 5x

^{4}– 6x

^{3}+ 4x – 12. See also.

**Leading coefficient**.

8

## What is the degree of the term?

**Degree of a Term**. For a

**term**with one variable, the

**degree**is the variable's exponent. With more than one variable, the

**degree**is the sum of the exponents of the variables.

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## What is a like term in math?

"

**Like terms**" are**terms**whose variables (and their exponents such as the 2 in x^{2}) are the same. In other words,**terms**that are "**like**" each other. Note: the coefficients (the numbers you multiply by, such as "5" in 5x) can be different.10

## Are A and AB like terms?

The

**like terms**are abc and acb;**ab and ba**. Note, abc and acb are identical and**ab and ba**are also identical. It does not matter in what order we multiply – for example, 3 x 2 x 4 is the same as 3 x 4 x 2. (c) –3a; –3ab; –3b There are no**like terms**in this example.11

## What is collecting terms?

**Collecting**like

**terms**. To simplify an expression, we

**collect**like

**terms**. Look at the expression: 4x + 5x -2 - 2x + 7. To simplify: The x

**terms**can be collected together to give 7x.

12

## What is the distributive property?

The

**distributive property**is one of the most frequently used**properties**in math. In general, this term refers to the**distributive property**of multiplication which states that the.**Definition**: The**distributive property**lets you multiply a sum by multiplying each addend separately and then add the products.13

## What does the term coefficient mean in math?

A number used to multiply a variable. Example: 6z means 6 times z, and "z" is a variable, so 6 is a

**coefficient**. Variables with no number have a**coefficient**of 1. Example: x is really 1x. Sometimes a letter stands in for the number.14

## What is the meaning of coefficient in math?

A number or symbol multiplied with a variable or an unknown quantity in an algebraic term. For

**example**, 4 is the**coefficient**in the term 4x, and x is the**coefficient**in x(a + b). A numerical**measure**of a physical or chemical property that is constant for a system under specified conditions.15

## What is the scientific definition of coefficient?

In math and

**science**, a**coefficient**is a constant term related to the properties of a product. In the equation that measures friction, for example, the number that always stays the same is the**coefficient**. In algebra, the**coefficient**is the number that you multiply a variable by, like the 4 in 4x=y.16

## What does a coefficient represent?

You must understand both in order to read and to use chemical equations successfully. First: the

**coefficients**give the number of molecules (or atoms) involved in the reaction. In the example reaction, two molecules of hydrogen react with one molecule of oxygen and produce two molecules of water.17

## How is a coefficient different from a subscript?

**Difference**Between a

**Coefficient**and a

**Subscript**.

**Coefficients**and

**subscripts**are essential components when writing longhand chemical formula compounds or equations. A

**coefficient**, reflecting the number of molecules in a given substance, is a number placed in front of a given molecule's abbreviation.

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## What is the Taylor rule for monetary policy?

That is, the

**rule**"recommends" a relatively high interest rate (a "tight"**monetary policy**) when inflation is above its target or when output is above its full-employment level, in order to reduce inflationary pressure.19

## Is MP as model?

**IS/MP model**. The

**IS/MP model**(Investment–Savings / Monetary–Policy) is a macroeconomic tool which displays short-run fluctuations in the interest rate, inflation and output.

20

## What is the Fisher equation in economics?

The

**Fisher equation**in financial mathematics and economics estimates the relationship between nominal and real interest rates under inflation. It is named after Irving**Fisher**, who was famous for his works on the theory of interest. In economics, this**equation**is used to predict nominal and real interest rate behavior.