Question

$$ \lim_{x \rightarrow a} f(x) \pm g(x)= \lim_{x \rightarrow a} f(x)\pm \lim_{x \rightarrow a} g(x)$$

$$=0 \pm 0=?$$

$$= \infty \pm \infty =?$$

$$= L_{1} \pm L_{2} =?$$

$$=0 \pm \infty =?$$

$$= \infty \pm0=?$$

$$=L \pm \infty =?$$

$$= \infty \pm L=?$$

$$=0 \pm L=?$$

$$=L \pm0=?$$

Answer 1

$0\pm 0=0$

$\infty+\infty=\infty$

$\infty-\infty$ مبهم است و باید رفع ابهام کرد.

$f(x)\pm g(x)\to L_1\pm L_2$

$0\pm\infty=\pm\infty$

$\infty\pm 0=\infty$

$L\pm\infty=\pm\infty$

$\infty\pm L=\infty $

$0\pm L=\pm L$

$L\pm 0=\pm 0$