Is there a reason MuPad doesn't find the obvious cancellation?
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I have:
f := 1/2* sqrt( 16-x^2 )
df := diff( f, x )
simplify( f * sqrt( 1 + df^2 ) )
mupad doesn't find the obvious cancellation (sqrt( 16-x^2 ) should go away)
Why not? Is there an algebraic reason I'm missing, or am I using the simplify function incorrectly, or is it something else?
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Matt Tearle
2011년 6월 17일
I'm guessing it's something to do with assumptions about squares and square roots, and maybe denominators. Wouldn't swear to it, though. If you want it to do what you'd probably do by hand, you can try this:
Simplify(f * sqrt( 1 + df^2 ),IgnoreAnalyticConstraints)
(Note the capital S)
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Walter Roberson
2011년 6월 17일
In particular sqrt(t) * sqrt(1/t) does not cancel if t is 0. Or in your case, if x = +/- 4
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