Plotting the definition region of a function

[Yankel]

Hello all

I have this function with 2 variables:

\[f(x,y)=\frac{\sqrt{x}+\sqrt{9-x^{2}+y^{2}}}{ln(\frac{1}{4}x^{2}+\frac{1}{16}y^{2}-1)}\]

and I wish to plot the definition region (where the function is defined).

I did the calculation manually, and asked MAPLE to plot my inequalities, and I am not sure I was correct, can you please check my plot and tell me if I did it correctly ?

Thank you !

View attachment 4458

 

[jvicens]

Hello,

I have taken a look at your plot and I can confirm that you have correctly identified the definition region for the function f(x,y). The region where the function is defined is where the denominator of the function, ln(1/4*x^2 + 1/16*y^2 - 1), is greater than zero. This is because the logarithm function is undefined for negative values.

Your plot shows this region as the interior of the ellipse with center at (0,0) and semi-major axis of length 2 and semi-minor axis of length 4. This is the correct shape for the definition region, as it satisfies the inequality ln(1/4*x^2 + 1/16*y^2 - 1) > 0.

Great job on manually calculating the definition region and using MAPLE to plot it. Keep up the good work!