As x approaches plus-or-minus infinity = limit of StartFraction 4 Over x Superscript 5 EndFraction as x approaches plus-or-minus infinity, so as x approaches infinity, g (x) approaches 0.

Function:

The function given is:

$g(x) = \frac{4x+9}{x^6+1}$

Limit as x goes to infinity:

To find the limit of a function as x goes to infinity, we consider the term with the highest exponent in the numerator and in the denominator. So

$\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} \frac{4x+9}{x^6+1} = \lim_{x \rightarrow \infty} \frac{4x}{x^6} = \lim_{x \rightarrow \infty} \frac{4}{x^5} = \frac{4}{\infty^5} = 0$

The graphic of the function, given at the end of this answer, corroborates the answer.

Thus, the correct option is:

As x approaches plus-or-minus infinity = limit of StartFraction 4 Over x Superscript 5 EndFraction as x approaches plus-or-minus infinity, so as x approaches infinity, g (x) approaches 0.

For more on limits as x approaches infinity, you can check brainly.com/question/12207599.

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