- #1

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- Homework Statement
- Decide if the limit exists.

- Relevant Equations
- $$\lim_{x^2+y^2 \rightarrow +\infty} {\frac {xy} {x^2+y^2}}$$

I'm not sure if the way I solve these limits is correct, so let me know if I'm doing something wrong.

$$\lim_{x^2+y^2 \rightarrow +\infty} {\frac {xy} {x^2+y^2}}$$

$$r = x^2+y^2$$

$$\lim_{r \rightarrow +\infty} {\frac {r\cdot cos(v) \cdot r \cdot sin(v)} r}$$

$$\lim_{r \rightarrow +\infty} {r\cdot cos(v)sin(v)} \rightarrow \infty$$Also how can I be sure if $$cos(v)\cdot sin(v)$$ will make this go to inf, -inf or even be undefined?

I havn't even defined v..

$$\lim_{x^2+y^2 \rightarrow +\infty} {\frac {xy} {x^2+y^2}}$$

$$r = x^2+y^2$$

$$\lim_{r \rightarrow +\infty} {\frac {r\cdot cos(v) \cdot r \cdot sin(v)} r}$$

$$\lim_{r \rightarrow +\infty} {r\cdot cos(v)sin(v)} \rightarrow \infty$$Also how can I be sure if $$cos(v)\cdot sin(v)$$ will make this go to inf, -inf or even be undefined?

I havn't even defined v..