Given the followning limit:
lim
To find limit I have made following steps:
- Let x = y ,then limit equals 0
- Let x > y ,then consider the limit:
\lim_{x \rightarrow \infty, y \rightarrow \infty} \left( \frac{x^2}{x^2 + y^2}\right)^{x^2} = \lim_{x \rightarrow \infty, y \rightarrow \infty} \left( \frac{1}{1 + \frac{y^2}{x^2}}\right)^{x^2} = 0
with respect to 0 < y^2/x^2 < const
- Let y > x ,then consider the limit:
\lim_{x \rightarrow \infty, y \rightarrow \infty} \left( \frac{x^2}{x^2 + y^2}\right)^{y^2} = \lim_{x \rightarrow \infty, y \rightarrow \infty} \left( \frac{1}{\frac{x^2}{y^2} + 1}\right)^{x^2} = 0
with respect to 0 < x^2/y^2 < const
What could you say about my solution?
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