Differentiation formula: Is this a typo?

In summary, the conversation is about a potential typo in a formula for estimating the error term in the Taylor series. The notes initially state that the error term is positive, but after substitution, it becomes negative. The question is whether this is a typo or if there is a theory behind it. It is concluded that the formula is for estimating the error term and the notation was initially confusing.
  • #1
maistral
240
17
TL;DR Summary
Resource found in the 'net, trying to know if this is a typo or not.
Red arrows.
1628420347688.png


The notes initially say that the error term is positive. After substitution of A and C which are clearly positive, the term suddenly became negative...? Is this a typo, or is there a theory behind this?
 
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  • #2
It seems OK observing that the third term of (5.14) is f”(x).
 
Last edited:
  • #3
anuttarasammyak said:
It seems OK observing that the third term of (5.14) is f”(x).
What does this imply? That either positive or negative will work?
 
  • #4
maistral said:
Summary:: Resource found in the 'net, trying to know if this is a typo or not.

Red arrows.
View attachment 287254

The notes initially say that the error term is positive. After substitution of A and C which are clearly positive, the term suddenly became negative...? Is this a typo, or is there a theory behind this?
It would seem to be the formula for an estimate of the error term in the Taylor series. Is this what your question was?
 
  • #5
forlmula(5.14).jpg


Transfer the second term of RHS to LHS.
 
Last edited:
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  • #6
I finally got it! The notation was so confusing, sorry.

1628619319082.png


1628619341009.png
 
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Likes anuttarasammyak and WWGD

What is a differentiation formula?

A differentiation formula is a mathematical expression that is used to calculate the rate of change of a function at a specific point. It is commonly used in calculus to find the derivative of a function.

How do you use a differentiation formula?

To use a differentiation formula, you first need to identify the function you want to differentiate. Then, you plug the function into the formula and simplify it to find the derivative at a specific point.

What is the purpose of a differentiation formula?

The purpose of a differentiation formula is to find the rate of change of a function at a specific point. This is useful in various fields of science and engineering, such as physics, economics, and engineering.

Is the differentiation formula the same as the derivative?

Yes, the differentiation formula is another name for the derivative. They both refer to the same concept of finding the rate of change of a function at a specific point.

Is the differentiation formula prone to typos?

Yes, like any mathematical formula, the differentiation formula is prone to typos. It is important to double-check your work and use proper notation to avoid mistakes when using the formula.

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