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December 21st, 2018, 02:56 AM   #1
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functions of several variables

How do I find the range for ln(9 - x^2 - y^2 - z^2)?
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Last edited by skipjack; December 21st, 2018 at 03:43 AM.
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December 21st, 2018, 03:44 AM   #2
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Can you make a guess as to what the range is?
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December 21st, 2018, 03:50 AM   #3
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i do know what the range so it wouldn't be a guess =)
but i don't understand how we got it.
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December 21st, 2018, 04:05 AM   #4
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Let $\displaystyle x^2+y^2+z^2=t^2$
$\displaystyle f(t)=\ln(9-t^2 )$ , by domain $\displaystyle |t|<3$
$\displaystyle \lim_{t\rightarrow 3} f(t)<f(t)\leq f(0)$
$\displaystyle -\infty < \ln(9-x^2-y^2-z^2)\leq \ln9$
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Last edited by skipjack; December 21st, 2018 at 06:04 AM.
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