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ALGEBRA in Calculus proof... Can you help me understand the basis for bringing delta x upstairs into only the numerator in this step of a problem?
 2 years ago
 2 years ago
ALGEBRA in Calculus proof... Can you help me understand the basis for bringing delta x upstairs into only the numerator in this step of a problem?
 2 years ago
 2 years ago

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FreeTraderBest ResponseYou've already chosen the best response.1
\[1/\Delta x * (\Delta u)v  u(\Delta v)/(v + \Delta v)v\] \[((\Delta u / \Delta x)v  u(\Delta v/\Delta x))/(v + \Delta v)v\]
 2 years ago

FreeTraderBest ResponseYou've already chosen the best response.1
This is from Lecture Session 10 of MIT OCW Math 18.01 Scholar  Single Variable Calculus.
 2 years ago

FreeTraderBest ResponseYou've already chosen the best response.1
The lecture and lecture notes show what I typed above. I don't understand why the Delta x would not have to be multiplied against the (v + Delta v)v term in the denominator.
 2 years ago

FreeTraderBest ResponseYou've already chosen the best response.1
How does the Delta x term get into the numerator of the numerator?
 2 years ago

TuringTestBest ResponseYou've already chosen the best response.1
\[{{1\overΔx}(Δu)v−u(Δv)\over(v+Δv)v} \to {{Δu \overΔx}v−u{Δv \overΔx}\over(v+Δv)v}\]is the step?
 2 years ago

FreeTraderBest ResponseYou've already chosen the best response.1
Almost. The 1/Delta x is a separate fraction. It started out as simply Delta x under everything else.
 2 years ago

FreeTraderBest ResponseYou've already chosen the best response.1
And then ended up as you have on the right hand side.
 2 years ago

FreeTraderBest ResponseYou've already chosen the best response.1
see attached for more clarity. It's near the bottom third of the page...
 2 years ago

TuringTestBest ResponseYou've already chosen the best response.1
oh this is simple: multiply out the bottom by delta x then divide the top and bottom by delta x much easier when I can see it!
 2 years ago

TuringTestBest ResponseYou've already chosen the best response.1
or divide top and bottom of \[{1\over \Delta x}\] by \[\Delta x\]you get\[{{1\over \Delta x}\over1}{(\Delta u)vu (\Delta v)\over(v+\Delta v)v}\]
 2 years ago

FreeTraderBest ResponseYou've already chosen the best response.1
I need to go to Algebra Tricks Boot Camp. Thanks.
 2 years ago

FreeTraderBest ResponseYou've already chosen the best response.1
I still think that is really funky. I will need to do some test problems to convince my rocklike brain this works just like you show it does.
 2 years ago
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