The problem is: \(\displaystyle\lim_{{{\left({x},{y},{z}\right)}\rightarrow{\left({0},{0},{0}\right)}}}{\frac{{{x}{y}+{2}{y}{z}+{3}{x}{z}}}{{{x}^{{2}}+{4}{y}^{{2}}+{9}{z}^{{2}}}}}\)

George Michael 2022-04-10 Answered
The problem is:
lim(x,y,z)(0,0,0)xy+2yz+3xzx2+4y2+9z2
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Answers (1)

ditumpasz9xj
Answered 2022-04-11 Author has 8 answers
Let's take the limit z0 first, getting
limx,y0xyx2+4y2
Now consider what happens if you take the limit along y=x
limx,y0xyx2+4y2=limx0x25x2=15
and along y=2x:
limx,y0xyx2+4y2=limx02x217x2=217
That's enough to tell you that the limit depends on direction.
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