Question

Which statement describes the behavior of the function f (x) = StartFraction 2 x Over 1 minus x squared EndFraction?

Answer 1

Answer:

B. The graph approaches 0 as x approaches infinity.

Step-by-step explanation:

Answer 2

Answer:

• Second option: the graph approaches 0 as x approaches infinity.

Explanation:

The function f(x) is:

$f(x)=\frac{2x}{1-x^2}$

• When x approach infinity the term x² grows rapidly (more rapid than x), thus 1 - x², which is in the denominator will decrease, become a large negative more rapid than the x in the numerator. Thus you can expect that the function approaches zero.

To prove that in a more analytical way, divide both numerator and denominator by x and simplifiy:

$\lim_{x \to \infty} \frac{2x}{1-x^2}\\\\ \lim_{x \to \infty} \frac{2x/x}{(1-x^2)/x}\\\\ \lim_{x \to \infty} \frac{2}{1/x-x}\\\\\lim_{x \to \infty} \frac{2}{0-x}\\ \\ \lim_{x \to \infty} \frac{2}{-x}\\ \\ \lim_{x \to \infty} -\frac{2}{x}=0$