In Calculus, does the limit somehow describe QP

In summary, in the world of calculus, the value of 'h' approaches zero but never actually reaches it. Assigning 'h' a value of zero would result in a nonsensical equation. This concept may reflect the principles of the quantum world. As 'h' approaches zero, it does so continuously rather than in jumps. The Planck length is the next higher value to zero in this scenario. Additionally, it is possible to obtain the laws of classical mechanics by manipulating the equations in this manner, as demonstrated by Shankar.
  • #1
hankaaron
83
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In calculus we say that the value 'h' approaches zero, but it is never zero. In fact if we assign 'h' the value zero, the equation becomes nonsensical.

Is this a reflection of the quantum world? Also as 'h' approaches zero, does it do so in jumps? Is the next higher value to zero a Planck length?
 
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  • #2
hankaaron said:
In calculus we say that the value 'h' approaches zero, but it is never zero. In fact if we assign 'h' the value zero, the equation becomes nonsensical.

Is this a reflection of the quantum world? Also as 'h' approaches zero, does it do so in jumps? Is the next higher value to zero a Planck length?

No it goes to zero. If you futz the equations right you get the laws of classical mechanics out when you do that. I believe Shankar does this somewhere.
 

FAQ: In Calculus, does the limit somehow describe QP

What is a limit in calculus?

A limit in calculus is a fundamental concept that describes the behavior of a function as its input approaches a specific value. It is used to determine the value that a function approaches as its input gets closer and closer to a given value. In other words, it is used to find the value that a function "approaches" but does not necessarily reach.

How do you find the limit of a function?

To find the limit of a function, the function must be evaluated at values that are very close to the given value. This is done by creating a table of values and using smaller and smaller values for the input. Another method is to use algebraic techniques, such as factoring or simplifying, to evaluate the limit. In some cases, the limit may not exist or may require advanced techniques to be evaluated.

What is the meaning of a limit in terms of a graph?

The limit of a function can be thought of as the y-value that the function approaches as the x-value approaches a specific value. In terms of a graph, this can be visualized as the y-value of a point that the function gets closer and closer to as the x-value gets closer and closer to a given value.

Can limits be used to find the slope of a tangent line?

Yes, limits can be used to find the slope of a tangent line. In fact, the derivative of a function is defined as the limit of the slope of a secant line as the two points on the line get closer and closer together. This is known as the limit definition of a derivative and is a fundamental concept in calculus.

How are limits used in real-life applications?

Limits are used in real-life applications in various fields such as physics, engineering, and economics. They are used to model and predict the behavior of systems, such as the trajectory of a projectile or the growth of a population. Limits are also used in optimization problems to find the maximum or minimum value of a function. Overall, limits play a crucial role in understanding and analyzing the real world using mathematical models.

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