As x tends to infinity the function [tex]f(x) = \frac{2x}{1-x^{2} }[/tex] approaches zero.
Given function is:
[tex]f(x) = \frac{2x}{1-x^{2} }[/tex]
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.
[tex]f(x) = \frac{2}{\frac{1}{x} -x}[/tex]
[tex]\lim_{x \to \infty} f(x) \\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x}[/tex]
As we know that as x approaches the infinity 1/x approaches 0.
So, [tex]\\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x} = \lim_{x \to \infty} \frac{2}{-x}[/tex]
[tex]\lim_{x \to \infty} \frac{-2}{x} =0[/tex]
Therefore, as x tends to infinity the function [tex]f(x) = \frac{2x}{1-x^{2} }[/tex] approaches zero.
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