Question 1208157
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The other tutors have done a great job. 
I know the instructions specifically state "no graphing", but let's look at a graph anyway to help verify the range is [0, 2/3] aka {{{0 <= y <= 2/3}}}


{{{graph(400,400,-4,4,-1.5,1.5,-100,(sqrt(4-x^2))/(sqrt(9-x^2)),2/3)}}}


The green curve is {{{h(x) = (f(x))/(g(x)) = (sqrt(4-x^2))/(sqrt(9-x^2))}}}
The blue horizontal line is y = 2/3 to help show the curve maxes out at this y value.


For some reason, the built-in algebra.com graphing tool shown above is glitching a bit. 
The part of the curve on the right needs to extend down to the point (2,0).
Perhaps a better look would be to use something like Desmos
<a href="https://www.desmos.com/calculator/nxfzbzullv">https://www.desmos.com/calculator/nxfzbzullv</a>


GeoGebra is another useful graphing tool.
There are many others.
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