Which statement best describes the limit shown below? lim_(x rarr oo)(x^(76))/(2(2)^(x)+3x^(76)) The limit equals zero The limit does not exist The limit exists and does not equal zero

Given Limit Expression: We are given the limit expression lim_(x -> ∞)(x^(76))/(2(2)^(x)+3x^(76)). To find the limit as x approaches infinity, we need to analyze the behavior of the numerator and the denominator separately.Analyze Numerator: The numerator is x^(76), which grows very large as x approaches infinity. However, we need to compare this growth with the growth of the denominator to determine the limit.Analyze Denominator: The denominator is 2(2)^(x) + 3x^(76). The term 2(2)^(x) grows exponentially as x approaches infinity, which is much faster than the polynomial growth of x^(76). Therefore, the exponential term will dominate the denominator as x becomes very large.Comparison of Growth: Since the exponential growth in the denominator is much faster than the polynomial growth in the numerator, the fraction as a whole will approach zero as x approaches infinity. This is because the denominator will become much larger than the numerator.Final Limit: Therefore, the limit of the function as x approaches infinity is 0. This means that the statement ＂The limit equals zero＂ best describes the limit of the given function.

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Which statement best describes the limit shown below?

lim_(x rarr oo)(x^(76))/(2(2)^(x)+3x^(76))
The limit equals zero
The limit does not exist
The limit exists and does not equal zero

Which statement best describes the limit shown below? $\newline$ $\lim _{x \rightarrow \infty} \frac{x^{76}}{2(2)^{x}+3 x^{76}}$ $\newline$ The limit equals zero $\newline$ The limit does not exist $\newline$ The limit exists and does not equal zero

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Q. Which statement best describes the limit shown below?

\newline

\lim _{x \rightarrow \infty} \frac{x^{76}}{2(2)^{x}+3 x^{76}}

\newline

The limit equals zero

\newline

The limit does not exist

\newline

The limit exists and does not equal zero

Given Limit Expression: We are given the limit expression $\lim_{x \to \infty}\left(\frac{x^{76}}{2(2)^{x}+3x^{76}}\right)$ . To find the limit as $x$ approaches infinity, we need to analyze the behavior of the numerator and the denominator separately.
Analyze Numerator: The numerator is $x^{76}$ , which grows very large as $x$ approaches infinity. However, we need to compare this growth with the growth of the denominator to determine the limit.
Analyze Denominator: The denominator is $2(2)^{x} + 3x^{76}$ . The term $2(2)^{x}$ grows exponentially as $x$ approaches infinity, which is much faster than the polynomial growth of $x^{76}$ . Therefore, the exponential term will dominate the denominator as $x$ becomes very large.
Comparison of Growth: Since the exponential growth in the denominator is much faster than the polynomial growth in the numerator, the fraction as a whole will approach $0$ as $x$ approaches infinity. This is because the denominator will become much larger than the numerator.
Final Limit: Therefore, the limit of the function as $x$ approaches $\infty$ is $0$ . This means that the statement ＂The limit equals zero＂ best describes the limit of the given function.