11. $$ f(x)=x^{6}+4 x^{3}-3 x $$ As $$ x \rightarrow+\infty $$

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As $$ x \rightarrow +\infty $$, $$ f(x) $$ approaches $$ +\infty $$. To analyze the behavior of the function $$ f(x) = x^6 + 4x^3 - 3x $$ as $$ x \rightarrow +\infty $$, we can focus on the leading term of the polynomial, which is the term with the highest degree. In this case, the leading term is $$ x^6 $$. As $$ x $$ approaches infinity, the other terms $$ 4x^3 $$ and $$ -3x $$ become negligible compared to $$ x^6 $$. Therefore, we can conclude that: $$ f(x) \sim x^6 \quad \text{as } x \rightarrow +\infty $$ This means that the function $$ f(x) $$ behaves like $$ x^6 $$ for very large values of $$ x $$. Thus, we can state: $$ \lim_{x \to +\infty} f(x) = +\infty $$ In summary, as $$ x \rightarrow +\infty $$, $$ f(x) $$ approaches $$ +\infty $$.

11. \( f(x)=x^{6}+4 x^{3}-3 x \) As \( x \rightarrow+\infty \)

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11. \( f(x)=x^{6}+4 x^{3}-3 x \) As \( x \rightarrow+\infty \)

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