which statement describes the behavior of the function $f(x)=\\frac{2x}{1 - x^{2}}$?\nthe graph approaches…

which statement describes the behavior of the function $f(x)=\\frac{2x}{1 - x^{2}}$?\nthe graph approaches $-2$ as $x$ approaches infinity.\nthe graph approaches $0$ as $x$ approaches infinity.\nthe graph approaches $1$ as $x$ approaches infinity.\nthe graph approaches $2$ as $x$ approaches infinity.

which statement describes the behavior of the function $f(x)=\\frac{2x}{1 - x^{2}}$?\nthe graph approaches $-2$ as $x$ approaches infinity.\nthe graph approaches $0$ as $x$ approaches infinity.\nthe graph approaches $1$ as $x$ approaches infinity.\nthe graph approaches $2$ as $x$ approaches infinity.

Answer

Answer:

The graph approaches (0) as (x) approaches infinity.

Explanation:

Step1: Dividir numerador y denominador por (x^{2})

$$\lim_{x\rightarrow\infty}\frac{2x}{1 - x^{2}}=\lim_{x\rightarrow\infty}\frac{\frac{2x}{x^{2}}}{\frac{1}{x^{2}}-\frac{x^{2}}{x^{2}}}$$

Step2: Simplificar la expresión

$$=\lim_{x\rightarrow\infty}\frac{\frac{2}{x}}{\frac{1}{x^{2}} - 1}$$

Step3: Calcular el límite

Como (\lim_{x\rightarrow\infty}\frac{2}{x}=0) y (\lim_{x\rightarrow\infty}\frac{1}{x^{2}} = 0), entonces: $$\lim_{x\rightarrow\infty}\frac{\frac{2}{x}}{\frac{1}{x^{2}} - 1}=\frac{0}{0 - 1}=0$$