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+--- Thread: Simplify symbolic equations based in assumptions (/thread-21952.html)
Simplify symbolic equations based in assumptions - Nick11014 - 06-26-2024 03:26 PM
I am trying to simplify a symbolic equation like ( x * y ) / ( x + y ) using the assume() function.
If y is much greater than x, then:
x + y = y;
( x * y ) / ( x + y ) = ( x * y ) / ( y ) = x
What i tried to do is something like
Code:
assume(y >> x ); // >> does not work. just for exemplification
simplify(( x * y ) / ( x + y )); // returns xIs this possible ?
RE: Simplify symbolic equations based in assumptions - C.Ret - 07-06-2024 07:18 PM
(06-26-2024 03:26 PM)Nick11014 Wrote: If y is much greater than x, then: x + y = y; ( x * y ) / ( x + y ) = ( x * y ) / ( y ) = xBonsoir,
When \( y \) is very large in front of \(x\), there is no real equality. One way to see things is to consider the asymptote form: \( \displaystyle \lim_{ x \ll y}\left(\frac{x\cdot y}{x+y}\right) = x \).
To obtain such a result on the HP Prime, one way is to use an extra CAS variable to symbolized the ratio \( r = \frac{x}{y}\). Having \( x \ll y \) is equivalent to have \(r\) approaching zero :
\( \displaystyle \lim_{ x \ll y}\left(\frac{x\cdot y}{x+y}\right) = \displaystyle \lim_{ r \to 0}\left(\frac{x\cdot y}{x+y}\right) = x \) where \( r = \frac{x}{y}\).
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