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Can you tell me if the method of evaluating this limit is right or wrong please?

The limit is:

[tex]\lim_{\substack{x\rightarrow 0\\y\rightarrow 0\\z\rightarrow 0}} f(x,y)=\frac{x^2+y^2-z^2}{x^2+y^2+z^2}[/tex]

I evaluate it along the x-axis, y-axis, and z-axis...

[tex]\lim_{\substack{x\rightarrow 0\\y=0\\z=0}} f(x,y)=\frac{x^2+y^2-z^2}{x^2+y^2+z^2}=\frac{x^2}{x^2}=1[/tex]

and similarly the limit along the y-axis is 1, and the limit along the z-axis is -1.

Since the limits do not equal, the limit DNE.

Is this right or is this wrong? Thank you for the help!

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# Homework Help: Quick limits Q

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