Undergrad Differentiation formula: Is this a typo?

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SUMMARY

The discussion centers on a potential typo in the differentiation formula related to the error term in the Taylor series. Initially, the notes indicate that the error term is positive; however, after substituting positive values for A and C, the term unexpectedly becomes negative. Participants clarify that this may not be a typo but rather a theoretical aspect of the formula, specifically referencing the third term of equation (5.14) as f”(x). The confusion arises from the notation used in the notes.

PREREQUISITES
  • Understanding of Taylor series and error terms
  • Familiarity with differentiation and notation in calculus
  • Knowledge of mathematical proofs and substitutions
  • Ability to interpret mathematical equations, specifically equation (5.14)
NEXT STEPS
  • Research the implications of error terms in Taylor series approximations
  • Study the notation and terminology used in advanced calculus
  • Examine the derivation and applications of f”(x) in differentiation
  • Explore common pitfalls in mathematical substitutions and their interpretations
USEFUL FOR

Mathematicians, students studying calculus, educators teaching differentiation concepts, and anyone involved in mathematical analysis or error estimation.

maistral
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TL;DR
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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It seems OK observing that the third term of (5.14) is f”(x).
 
Last edited:
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?
 
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?
 
forlmula(5.14).jpg


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

1628619319082.png


1628619341009.png
 
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