Calculus Problem

Mathmasteriw

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Oct 22, 2020
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Hi guys and girls,
Can anyone double check my work here?
I belive I am correct here.
Differentiate the funcion with respect to ‘t’ and have shown the ‘rate of change’ when t is 5
Thanks for your time 😀
0E4596C0-ED47-4E1F-BFA8-B9DD83D83EB9.jpeg
 

skeeter

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looks fine
 

Otis

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\(\displaystyle \frac{dv}{dt}(5)\) …
Hi Mathmasteriw. That's an interesting form of function notation that I've never seen before. I'm curious. Where did you see it?

😎
 

HallsofIvy

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I have seen that in many places.
\(\displaystyle \frac{dv}{dt}(5)= \frac{dv(5)}{dt}\).
meaning the derivative of v with respect to t, evaluated at t=5
Some people would prefer the first to the second on the grounds that the second could be interpreted as the derivative of the constant v(5) which is, of course, 0.
 

Jomo

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Personally I think the answer is (dv/dt)(5) = -2e^(-2.5) or -2/e^2.5. -.164 is an approximation and not the exact answer.
 

Otis

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… -0.164 is an approximation and not the exact answer.
Good point, Jomo, but we don't know for sure what the given instructions may have said.

😎
 

Otis

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I have seen that [derivative notation] in many places …
Thanks, Halls. It prompted me to think of and ponder this:

\[\frac{\text{dv}}{\text{dt}} \bigg\rvert_{5} = -0.164\]

I've never seen that done, either, but it makes sense.

… Some people would prefer [\( \; \frac{dv}{dt}(5) \; \)] to [\( \; \frac{dv(5)}{dt} \; \)] …
Agree!

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Jomo

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How I look at it is that \(\displaystyle \dfrac{dv}{dt}\) is a function of t. Just because the name of the function is a bit strange looking does not change its notion. \(\displaystyle \dfrac{dv}{dt}=\dfrac{dv}{dt}(t)\) and \(\displaystyle \dfrac{dv}{dt}\) evaluated at t= 5 is denoted as \(\displaystyle \dfrac{dv}{dt}(5)\).

I have used this notation frequently. I have also seen \(\displaystyle \dfrac{dv}{dt}(5)\) written as \(\displaystyle \dfrac{dv}{dt}|_{t=5}\)
 

Mathmasteriw

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Oct 22, 2020
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Hi Mathmasteriw. That's an interesting form of function notation that I've never seen before. I'm curious. Where did you see it?

😎
I owe a lot to what I have learned to this page 😀😎
 

topsquark

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\(\displaystyle \dfrac{dv}{dt}|_{t=5}\)
If memory serves me I've seen this in many forms in Math texts but the above quote is the only way I've seen Physicists write it.

-Dan
 
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