Using calculus to verify

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In summary, the conversation discusses using calculus to verify that v(t) = sqrt(gm/cd)tanh((sqrt(gcd/m)t) is a solution to dv/dt=g-(cd/m)v2. It is clarified that the focus is not on finding the solution, but rather verifying it. It is also mentioned that the listed question differs from the actual confusion in understanding.
  • #1
strawberryy
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I'm supposed to use calculus to verify that v(t) = sqrt(gm/cd)tanh((sqrt(gcd/m)t)

is a solution to dv/dt=g-(cd/m)v2. I don't understand what was done to achieve the solution.
 
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  • #2
While the derivation isn't hard, you aren't being asked to solve the differential equation as if you had no guess at the form of the solution space -- you are simply being asked to verify that that is a solution.
 
  • #3
Agreed, what you list as a question is different than what you actually profess confusion in understanding.

The question wants you to verify v(t) is a solution. Did you misunderstand, or did you really wish to discuss how to obtain that solution?
 

1. How does calculus help in verifying scientific theories?

Calculus is a branch of mathematics that deals with the study of continuous change and its applications. It provides a framework for understanding and analyzing complex systems, making it a valuable tool for verifying scientific theories. By using calculus, scientists can model and predict the behavior of natural phenomena, allowing them to test the validity of their theories.

2. Can calculus be used to verify experimental data?

Yes, calculus can be used to verify experimental data. By taking the derivative or integral of a function that represents the data, scientists can compare the results with the actual data points. If they match, it provides evidence that the data is accurate and supports the underlying theory.

3. What are the limitations of using calculus to verify theories?

One limitation of using calculus to verify theories is that it relies on mathematical models, which may not always accurately represent real-world phenomena. Additionally, the assumptions and simplifications made in these models can also impact the accuracy of the results. Therefore, it is important for scientists to carefully consider the limitations of their models when using calculus to verify theories.

4. Can calculus be used to verify all scientific theories?

No, calculus may not be applicable to all scientific theories. Some theories may not involve continuous change or may not have a mathematical representation that can be analyzed using calculus. In these cases, other methods of verification may be necessary.

5. How does the use of calculus in scientific research benefit society?

The use of calculus in scientific research has led to many advancements in technology and medicine, which have greatly benefited society. By accurately verifying scientific theories, calculus helps to improve our understanding of the natural world and allows us to make more informed decisions for the betterment of society.

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