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 3 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?
 3 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?

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

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

FreeTrader
 3 years ago
Best ResponseYou've already chosen the best response.1The 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.

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

TuringTest
 3 years ago
Best 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?

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

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

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

TuringTest
 3 years ago
Best ResponseYou've already chosen the best response.1oh 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!

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

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

FreeTrader
 3 years ago
Best ResponseYou've already chosen the best response.1I 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.
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