Question

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

A. The graph approaches –2 as x approaches infinity.
B. The graph approaches 0 as x approaches infinity.
C. The graph approaches 1 as x approaches infinity.
D. The graph approaches 2 as x approaches infinity.

Answer 1

Answer:

Option B.

Step-by-step explanation:

The given function is

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

We have find the behavior of the function f (x) as  x approaches infinity.

The given function can be rewritten as

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

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

$lim_{x\rightarrow \infty}f(x)=lim_{x\rightarrow \infty}\dfrac{2}{x(\dfrac{1}{x^2}-1)}$

Apply limit.

$lim_{x\rightarrow \infty}f(x)=\dfrac{2}{\infty(\dfrac{1}{\infty^2}-1)}$

$lim_{x\rightarrow \infty}f(x)=0$

The graph approaches 0 as x approaches infinity.

Therefore, he correct option is B.

Answer 2

Answer:

It's B on edge

Step-by-step explanation: