Which statement best describes the limit shown below? lim_(x rarr oo)(x^(2)+x^(68))/(x^(68)) The limit equals zero The limit does not exist The limit exists and does not equal zero

Divide Terms by x^68: We are given the limit expression lim_(x -> ∞)(x^2 + x^68) / x^68. To find the limit as x approaches infinity, we can divide each term in the numerator by x^68.Evaluate x^(-66): Divide x^2 by x^68 to get x^(2-68) = x^(-66). As x approaches infinity, x^(-66) approaches 0.Evaluate x^0: Divide x^68 by x^68 to get x^(68-68) = x^0 = 1. As x approaches infinity, this term remains 1.Combine Results: Combine the results of the division to rewrite the limit expression as lim_(x -> ∞)(0 + 1).Simplify Expression: Simplify the expression to get the limit as x approaches infinity of 1, which is simply 1.

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Which statement best describes the limit shown below?

lim_(x rarr oo)(x^(2)+x^(68))/(x^(68))
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? $\newline$ $\lim _{x \rightarrow \infty} \frac{x^{2}+x^{68}}{x^{68}}$ $\newline$ 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^{2}+x^{68}}{x^{68}}

\newline

The limit equals zero

\newline

The limit does not exist

\newline

The limit exists and does not equal zero

Divide Terms by $x^{68}$ : We are given the limit expression $\lim_{x \to \infty}(x^2 + x^{68}) / x^{68}$ . To find the limit as $x$ approaches infinity, we can divide each term in the numerator by $x^{68}$ .
Evaluate $x^{-66}$ : Divide $x^2$ by $x^{68}$ to get $x^{2-68} = x^{-66}$ . As $x$ approaches infinity, $x^{-66}$ approaches $0$ .
Evaluate $x^0$ : Divide $x^{68}$ by $x^{68}$ to get $x^{68-68} = x^0 = 1$ . As $x$ approaches infinity, this term remains $1$ .
Combine Results: Combine the results of the division to rewrite the limit expression as $\lim_{x \to \infty}(0 + 1)$ .
Simplify Expression: Simplify the expression to get the limit as $x$ approaches infinity of $1$ , which is simply $1$ .