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December 21st, 2018, 02:56 AM  #1 
Newbie Joined: Dec 2018 From: egypt Posts: 3 Thanks: 0  functions of several variables
How do I find the range for ln(9  x^2  y^2  z^2)? Thanks. Last edited by skipjack; December 21st, 2018 at 03:43 AM. 
December 21st, 2018, 03:44 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,467 Thanks: 2038 
Can you make a guess as to what the range is?

December 21st, 2018, 03:50 AM  #3 
Newbie Joined: Dec 2018 From: egypt Posts: 3 Thanks: 0 
i do know what the range so it wouldn't be a guess =) but i don't understand how we got it. 
December 21st, 2018, 04:05 AM  #4 
Senior Member Joined: Dec 2015 From: iPhone Posts: 474 Thanks: 73 
Let $\displaystyle x^2+y^2+z^2=t^2$ $\displaystyle f(t)=\ln(9t^2 )$ , by domain $\displaystyle t<3$ $\displaystyle \lim_{t\rightarrow 3} f(t)<f(t)\leq f(0)$ $\displaystyle \infty < \ln(9x^2y^2z^2)\leq \ln9$ Last edited by skipjack; December 21st, 2018 at 06:04 AM. 

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