Which statement best describes the limit shown below? lim_(x rarr oo)(x^(14))/(x^(73)) 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^(14))/(x^(73)). To find the limit as x approaches infinity, we need to analyze the behavior of the function.Simplify by Subtracting Exponents: We can simplify the expression by subtracting the exponents of x in the numerator and the denominator since they have the same base and we are dividing them. lim_(x -> ∞)(x^(14))/(x^(73)) = lim_(x -> ∞) x^(14-73)Analysis of Function Behavior: After subtracting the exponents, we get: lim_(x -> ∞) x^(-59) This means that as x approaches infinity, the function is x raised to the power of negative fifty-nine.Negative Exponent Interpretation: A negative exponent means that the function is the reciprocal of x raised to the positive exponent. Therefore, x^(-59) is equivalent to 1/(x^(59)). lim_(x -> ∞) x^(-59) = lim_(x -> ∞) 1/(x^(59))Approaching Zero: As x approaches infinity, the denominator x^(59) becomes larger and larger, making the whole fraction smaller and smaller, approaching zero. lim_(x -> ∞) 1/(x^(59)) = 0

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Which statement best describes the limit shown below?

lim_(x rarr oo)(x^(14))/(x^(73))
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? $\newline$ $\lim _{x \rightarrow \infty} \frac{x^{14}}{x^{73}}$ $\newline$ 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^{14}}{x^{73}}

\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 $\lim_{x \to \infty}\left(\frac{x^{14}}{x^{73}}\right)$ . To find the limit as $x$ approaches infinity, we need to analyze the behavior of the function.
Simplify by Subtracting Exponents: We can simplify the expression by subtracting the exponents of $x$ in the numerator and the denominator since they have the same base and we are dividing them. $\newline$ $\lim_{x \to \infty}(x^{14})/(x^{73}) = \lim_{x \to \infty} x^{14-73}$
Analysis of Function Behavior: After subtracting the exponents, we get: $\newline$ $\lim_{x \to \infty} x^{-59}$ $\newline$ This means that as $x$ approaches infinity, the function is $x$ raised to the power of negative fifty-nine.
Negative Exponent Interpretation: A negative exponent means that the function is the reciprocal of $x$ raised to the positive exponent. Therefore, $x^{-59}$ is equivalent to $1/(x^{59})$ . $\newline$ $\lim_{x \to \infty} x^{-59} = \lim_{x \to \infty} 1/(x^{59})$
Approaching Zero: As $x$ approaches infinity, the denominator $x^{59}$ becomes larger and larger, making the whole fraction smaller and smaller, approaching zero. $\newline$ $\lim_{x \to \infty} \frac{1}{x^{59}} = 0$