Which statement best describes the limit shown below? lim_(x rarr oo)(9x^(61))/(-9x^(61)+x^(60)) The limit equals zero The limit does not exist The limit exists and does not equal zero

Identify Powers: We are given the limit expression lim_(x → ∞)(9x^(61))/(-9x^(61)+x^(60)). To find the limit as x approaches infinity, we need to analyze the behavior of the numerator and the denominator separately.Factor Out x^(61): First, let's look at the highest power of x in both the numerator and the denominator. In this case, the highest power of x is 61 in both terms.Simplify Expression: We can factor out x^(61) from both the numerator and the denominator to simplify the expression. This gives us: lim_(x → ∞)(9x^(61))/(-9x^(61)+x^(60)) = lim_(x → ∞)(9)/(1 - (1/x))Evaluate Limit: As x approaches infinity, the term (1/x) approaches zero. Therefore, the expression simplifies to: lim_(x → ∞)(9)/(1 - (1/x)) = 9/(1 - 0) = 9/1 = 9Final Conclusion: The limit exists and does not equal zero. The correct statement is ＂The limit exists and does not equal zero.＂

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Which statement best describes the limit shown below?

lim_(x rarr oo)(9x^(61))/(-9x^(61)+x^(60))
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? $\newline$ $\lim _{x \rightarrow \infty} \frac{9 x^{61}}{-9 x^{61}+x^{60}}$ $\newline$ 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{9 x^{61}}{-9 x^{61}+x^{60}}

\newline

The limit equals zero

\newline

The limit does not exist

\newline

The limit exists and does not equal zero

Identify Powers: We are given the limit expression $\lim_{x \to \infty}(9x^{61})/(-9x^{61}+x^{60})$ . To find the limit as $x$ approaches infinity, we need to analyze the behavior of the numerator and the denominator separately.
Factor Out $x^{61}$ : First, let's look at the highest power of $x$ in both the numerator and the denominator. In this case, the highest power of $x$ is $61$ in both terms.
Simplify Expression: We can factor out $x^{61}$ from both the numerator and the denominator to simplify the expression. This gives us: $\newline$ $\lim_{x \to \infty}\frac{9x^{61}}{-9x^{61}+x^{60}} = \lim_{x \to \infty}\frac{9}{1 - \frac{1}{x}}$
Evaluate Limit: As $x$ approaches infinity, the term $(1/x)$ approaches zero. Therefore, the expression simplifies to: $\lim_{x \to \infty}\left(\frac{9}{1 - \left(\frac{1}{x}\right)}\right) = \frac{9}{1 - 0} = \frac{9}{1} = 9$
Final Conclusion: The limit exists and does not equal $0$ . The correct statement is ＂The limit exists and does not equal $0$ .＂