Question

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

The graph approaches –2 as x approaches infinity.
The graph approaches 0 as x approaches infinity.
The graph approaches 1 as x approaches infinity.
The graph approaches 2 as x approaches infinity.

Answer 1

b

Step-by-step explanation:

got it riht

Answer 2

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

Step-by-step explanation:

The function f(x) is:

`f(x)=(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) (2x)/(1-x^2)\\\\ \lim_(x \to \infty) (2x/x)/((1-x^2)/x)\\\\ \lim_(x \to \infty) (2)/(1/x-x)\\\\\lim_(x \to \infty) (2)/(0-x)\\ \\ \lim_(x \to \infty) (2)/(-x)\\ \\ \lim_(x \to \infty) -(2)/(x)=0`