Sentence in English in textbook "Calculus", by Robert A. Adams

In summary, the conversation was about a Spanish translation of a calculus book and a question about the title and a sentence in English from a specific section. The section was identified as "Velocity and Acceleration" and the sentence discussed the Mean Value Theorem and its equivalent version, Rolle's Theorem. The conversation also touched on the difference between the English words "mean" and "intermediate" and their corresponding mathematical theorems.
  • #1
mcastillo356
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Hi, PF

I've got a translation into spanish of the sixth edition of "Calculus", by Robert A. Adams. At the second chapter, "Differentiation", eleventh section, I would like to know: the title of the section (Could it be "Velocity and Acceleration"?); and a sentence of the Example 2 ("A point P moves along the x axis..."): at the solution of the question (d), I have something like "Velocity is continuous for all t, so, according to the Mean value theorem...". Wich would be the sentence in English?

Thanks!
 
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  • #2
The velocity is continuous for all t so, by the Intermediate-Value Theorem, has a constant sign on the intervals between the points where it is 0.
 
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  • #3
In my edition, it mentioned Mean Value Theorem, and it didn't make sense.

Greetings!
 
  • #4
Yeah, it's probably easy to mix up 'Teorema del valor medio' and 'Teorema del valor intermedio'.
 
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  • #5
The English word "mean" refers to an average, so the mean value theorem talks about the average value.
 
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  • #6
actually every derivative, continuous or not, has the intermediate value property, and the proof uses the mean value theorem, or at least its equivalent version, rolle's theorem. ( a function that goes up and then down, must take the same value twice and hence must level off somewhere in between.) so many interpretations are possible.
 
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Related to Sentence in English in textbook "Calculus", by Robert A. Adams

1. What is the purpose of learning calculus?

The purpose of learning calculus is to understand and analyze the behavior of functions and their rates of change. It is a fundamental tool in many fields of science and engineering, as well as a building block for more advanced mathematical concepts.

2. What are the main topics covered in a calculus textbook?

A typical calculus textbook covers topics such as limits, derivatives, integrals, and applications of these concepts to real-world problems. It may also include topics such as sequences, series, and multivariable calculus.

3. How can calculus be applied in everyday life?

Calculus has many practical applications in fields such as physics, engineering, economics, and statistics. It can be used to model and analyze real-world situations, make predictions, and optimize systems.

4. Is calculus difficult to learn?

While calculus may seem intimidating at first, it is a logical and systematic subject that can be learned with practice and dedication. It is important to have a strong foundation in algebra and trigonometry before learning calculus.

5. How can I succeed in learning calculus?

To succeed in learning calculus, it is important to attend class regularly, take good notes, and practice solving problems. It can also be helpful to seek out additional resources such as online tutorials or study groups.

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