Which statement best describes the limit shown below? lim_(x rarr oo)(-3(2)^(x))/(5log_(2)x) 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 -> ∞)(-3(2)^(x))/(5log_(2)x). To analyze the behavior of this limit, we need to consider the growth rates of the numerator and the denominator as x approaches infinity.Analysis of Growth Rates: The numerator -3(2)^(x) grows exponentially as x approaches infinity. Exponential functions grow much faster than polynomial or logarithmic functions.Numerator Behavior: The denominator 5log_(2)x is a logarithmic function, which grows much slower than the exponential function in the numerator. As x approaches infinity, the logarithmic function increases without bound, but at a much slower rate than the exponential function.Denominator Behavior: Since the numerator grows much faster than the denominator, the fraction as a whole will grow without bound. However, because the numerator is negative, the fraction will tend toward negative infinity.Limit Conclusion: Therefore, the limit does not exist because the expression diverges to negative infinity. The correct statement is ＂The limit does not exist.＂

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Which statement best describes the limit shown below?

lim_(x rarr oo)(-3(2)^(x))/(5log_(2)x)
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? $\newline$ $\lim _{x \rightarrow \infty} \frac{-3(2)^{x}}{5 \log _{2} x}$ $\newline$ 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{-3(2)^{x}}{5 \log _{2} x}

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The limit equals zero

\newline

The limit does not exist

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The limit exists and does not equal zero

Given Limit Expression: We are given the limit expression $\lim_{x \to \infty}\left(\frac{-3(2)^{x}}{5\log_{2}x}\right)$ . To analyze the behavior of this limit, we need to consider the growth rates of the numerator and the denominator as $x$ approaches infinity.
Analysis of Growth Rates: The numerator $-3(2)^{x}$ grows exponentially as $x$ approaches infinity. Exponential functions grow much faster than polynomial or logarithmic functions.
Numerator Behavior: The denominator $5\log_{2}x$ is a logarithmic function, which grows much slower than the exponential function in the numerator. As $x$ approaches infinity, the logarithmic function increases without bound, but at a much slower rate than the exponential function.
Denominator Behavior: Since the numerator grows much faster than the denominator, the fraction as a whole will grow without bound. However, because the numerator is negative, the fraction will tend toward negative infinity.
Limit Conclusion: Therefore, the limit does not exist because the expression diverges to negative infinity. The correct statement is ＂The limit does not exist.＂