Question

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

Answer 1

As x tends to infinity the function $f(x) = \frac{2x}{1-x^{2} }$ approaches zero.

Given function is:

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

What is a function?

A function f(x) is a rule which relates two variables where x and y are independent and dependent variables.

Divide the numerator and denominator of the given function by x.

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

$\lim_{x \to \infty} f(x) \\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x}$

As we know that as x approaches the infinity 1/x approaches 0.

So, $\\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x} = \lim_{x \to \infty} \frac{2}{-x}$

$\lim_{x \to \infty} \frac{-2}{x} =0$

Therefore, as x tends to infinity the function $f(x) = \frac{2x}{1-x^{2} }$ approaches zero.

To get more about functions visit:

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