Find the limist if it exists for a 3-variable function

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Homework Statement


lim(e^(-x*y) * sin( pi * z/2) as (x,y,z) approaches (3,0,1)

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The Attempt at a Solution


i know how to find the limit exists or not for a 2-variable function which is just set x=o;y=0;x=y
how can this method applies here
 
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Remember that the first approach when computing any limit is to just substitute the point that you are approaching.
 
n!kofeyn said:
Remember that the first approach when computing any limit is to just substitute the point that you are approaching.

And think about whether the function is continuous there, right?
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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