Kainui
  • Kainui
What is the difference between Delta x and dx?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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amistre64
  • amistre64
infinity
anonymous
  • anonymous
\[\Delta x \] means the change in x where dx is the derivative of x
amistre64
  • amistre64
when Delta x reaches infinity it becomes dx; the ghost of a departed ratio

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Kainui
  • Kainui
So when you multiply something by dx, what does that mean essentially?
amistre64
  • amistre64
it means that you are relating it back to when it had a real value
amistre64
  • amistre64
you might need to example that multiply by dx bit tho for clarity
Kainui
  • Kainui
So dx is a "ghost" ratio, basically a ratio with 0 in the denominator... but not quite... and multiplying that times something gives you a value based on... I mean, I know that's the integral but I'm still not sure I understand it.
amistre64
  • amistre64
2x dx for example is meaningless on its own we need more to the notation
amistre64
  • amistre64
{S} () dx is an operator on a derivative telling us that "x" was the important stuff
amistre64
  • amistre64
{S} (2x) dx means that we can undo this derivative to find out where it came from
amistre64
  • amistre64
or at least a family of functions from which it came; {S} (2x) dx = x^2 + C where C is some arbitrary constant relating this to a family of functions
Kainui
  • Kainui
\[dy=\int\limits_{}^{}dx\]\[dy/dx = 1\] Those are essentially the same thing, but why does it just work like dividing or multiplying?
amistre64
  • amistre64
\[\frac{dy}{dx}=1\] becasue its a ration at heart can be split into the form \[dy=1 dx\] which is meaningless without the \(\int\) symbol
amistre64
  • amistre64
\[\int dy = \int 1dx\] \[y=x+c\]
Kainui
  • Kainui
Hmm so why does there have to be an S symbol if it's multiplied by dx? I mean, I know you need some way of showing that there is a place to go from for definite integrals, but why have the symbol for indefinite integrals? What does the S symbol mean by itself with no dx around?
amistre64
  • amistre64
it represents an elongated "s" reminding us that an integration is the sum of the derivative parts - with respect to (*): d*
amistre64
  • amistre64
\[\sum_{0}^{\inf}f(x)\Delta x\implies\int_{0}^{inf}f(x)dx\] the summation is for discrete functions; the integral is for continuous functions
Kainui
  • Kainui
Ok, that makes sense, so it is literally just the exact same thing as saying the limit of an infinite riemann sum of infinitely small values...?
amistre64
  • amistre64
yes, whereas the Reimann is a discrete count; the integration is a contiuous count
Kainui
  • Kainui
Ok, I think that makes sense, leibniz notation is kinda weirding me out still, I'll sit and think about it a little longer. Thanks.
amistre64
  • amistre64
good luck :)

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