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Calculus help

The relationship of a capacitor voltage (volts) and time (seconds) is given by V=100(1-e^-0.1t). Plot the graph between t = 0 and t = 50 at 10 intervals.
Find the differentiation value at t = 10. Use calculus to verify your solution.

So I've drawn the graph and found the differentiation value. I just don't know how to verify it using calculus.

Any help will be appreciated :smile:
(edited 7 years ago)
Original post by OGGUS
The relationship of a capacitor voltage (volts) and time (seconds) is given by V=100(1-e^-0.1t). Plot the graph between t = 0 and t = 50 at 10 intervals.
Find the differentiation value at t = 10. Use calculus to verify your solution.

So I've drawn the graph and found the differentiation value. I just don't know how to verify it using calculus.

Any help will be appreciated :smile:


Not quite sure what you mean really, but just differentiate the relationship with respect to time, plug in 10 (provided it's in seconds) and see what you get.

When you say you 'found the differentiation value', do you mean using a graphical estimate to estimate the gradient at t = 10?
Reply 2
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OGGUS
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Original post by kingaaran
Not quite sure what you mean really, but just differentiate the relationship with respect to time, plug in 10 (provided it's in seconds) and see what you get.

When you say you 'found the differentiation value', do you mean using a graphical estimate to estimate the gradient at t = 10?


no it's the value I got when I differentiated the equation and plugged in 10.
Original post by OGGUS
no it's the value I got when I differentiated the equation and plugged in 10.


Then I don't know how you can go on to 'use calculus' because you've already used calculus by differentiating?
Reply 4
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Pangol
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I think that what they are expecting you to do is draw a tangent to the curve at t = 10 and find it's gradient - this is what they mean by "find the differentiation value at t = 10". Verifying using calculus is doing it the proper way!
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OGGUS
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Original post by kingaaran
Then I don't know how you can go to 'use calculus' because you've already used calculus by differentiating?

ok okay thanks
Reply 6
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OGGUS
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Original post by Pangol
I think that what they are expecting you to do is draw a tangent to the curve at t = 10 and find it's gradient - this is what they mean by "find the differentiation value at t = 10". Verifying using calculus is doing it the proper way!

I'll try that then thanks :smile:

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