How Do You Calculate Instantaneous Rate of Change in an Electrical Circuit?

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Homework Help Overview

The discussion revolves around calculating the instantaneous rate of change of an electrical current in a circuit, represented by the function C=(3s^3-s^2+5s)/(s^3+10), where C is the current and s is time in seconds. The original poster seeks clarification on how to approach finding the instantaneous rate of change at a specific time, as well as identifying vertical asymptotes.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster has successfully calculated the average rate of change but expresses confusion regarding the instantaneous rate of change. Some participants suggest that this involves taking the derivative, while others clarify the meaning of the derivative and its relation to limits. There is also a question about applying the form (x, x+h) for the derivative calculation.

Discussion Status

The discussion is ongoing, with participants providing guidance on the concept of derivatives and their application to the problem. There is recognition of the original poster's progress in calculating the average rate of change, but uncertainty remains regarding the derivative and its calculation.

Contextual Notes

Participants note that understanding derivatives is essential for solving the problem, and there is acknowledgment that the algebra involved may be complex due to the nature of the rational function presented.

ArielM
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Hi everyone, i am new to this website and i would like to ask one question that i don't quite get.
we have started a new topic in class about rates of change


Homework Statement


An Electrical current in a cicruit varies with time according to C=(3s^3-s^2+5s)/(S^3+10)
where currenct is "C" and time is "s" in seconds.

a) find the average rate of change from 0.75 seconds to 1.5 second
b)find the instantanious rate of change at 1.5 second.
c)Identify any vertical asymptotes.

Homework Equations





The Attempt at a Solution


I have managed to solved part a by substituting the values 0.75 and 1.5 to the equation.
i then took both answers and found the average rate of change by the formula y2-y1/x2-x1 (correct me if I am wrong)

as for finding the instanatnious rate of change - i am completley clueless :(
Thanks in advance !

Ariel Melichovich
 
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Welcome to PF!

Hi Ariel! Welcome to PF! :smile:
ArielM said:
n Electrical current in a cicruit varies with time according to C=(3s^3-s^2+5s)/(S^3+10)
where currenct is "C" and time is "s" in seconds.
…
as for finding the instanatnious rate of change - i am completley clueless :(

Instantaneous rate of change is the derivative, dC/ds. :smile:
 


tiny-tim said:
Hi Ariel! Welcome to PF! :smile:


Instantaneous rate of change is the derivative, dC/ds. :smile:

Thank you for your reply !
however, i am not quite sure what does the term 'd' mean. is that the derivative?

can the form (x,x+h) be apllied to this question where at the end i divide the equation by "h"?

Thanks again !
 
If you do not know how to find a derivative, then you cannot do this problem. The derivative is the "instantaneous rate of change". But from what you say, you seem to have heard of the basics of the derivative: it is the limit, as h goes to 0, of the average rate of change from x to x+ h. However, for the rational function you have, that is going to be a difficult algebraic calculation.

Your calculation of the average rate of change is correct
 

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