Which statement best describes the limit shown below? lim_(x rarr oo)(ln x)/(x^(46)+10x^(91)) 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 -> ∞)(ln x)/(x^(46)+10x^(91)). To determine the behavior of this limit, we need to analyze the growth rates of the numerator and the denominator as x approaches infinity.Analysis of Growth Rates: The numerator ln x grows logarithmically, which is much slower than any positive power of x. The denominator has two terms: x^(46) and 10x^(91). As x approaches infinity, the term with the highest power of x will dominate the growth of the denominator. In this case, it's the 10x^(91) term.Comparison of Numerator and Denominator: Since the denominator grows much faster than the numerator, the fraction as a whole will approach zero as x approaches infinity. This is because the denominator's growth will make the fraction's value smaller and smaller.Conclusion: Therefore, the correct statement that describes the limit is: ＂The limit equals zero.＂

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Which statement best describes the limit shown below?

lim_(x rarr oo)(ln x)/(x^(46)+10x^(91))
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? $\newline$ $\lim _{x \rightarrow \infty} \frac{\ln x}{x^{46}+10 x^{91}}$ $\newline$ 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{\ln x}{x^{46}+10 x^{91}}

\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 $\lim_{x \to \infty}\frac{\ln x}{x^{46}+10x^{91}}$ . To determine the behavior of this limit, we need to analyze the growth rates of the numerator and the denominator as $x$ approaches infinity.
Analysis of Growth Rates: The numerator $\ln x$ grows logarithmically, which is much slower than any positive power of $x$ . The denominator has two terms: $x^{46}$ and $10x^{91}$ . As $x$ approaches infinity, the term with the highest power of $x$ will dominate the growth of the denominator. In this case, it's the $10x^{91}$ term.
Comparison of Numerator and Denominator: Since the denominator grows much faster than the numerator, the fraction as a whole will approach $0$ as $x$ approaches infinity. This is because the denominator's growth will make the fraction's value smaller and smaller.
Conclusion: Therefore, the correct statement that describes the limit is: ＂The limit equals $0$ .＂