Find lim_(x rarr oo)(-5x^(4)+2x)/(x^(3)). Choose 1 answer: (A) 2 (B) 0 (C) -5 (D) The limit is unbounded

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Find  lim_(x rarr oo)(-5x^(4)+2x)/(x^(3)). Choose 1 answer: (A) 2 (B) 0 (C) -5 (D) The limit is unbounded

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Analyze Behavior: To find the limit of the given function as x approaches infinity, we need to analyze the behavior of the numerator and the denominator separately. The highest power of x in both the numerator and the denominator will dominate the behavior of the function as x becomes very large.Divide by Highest Power: The highest power of x in the numerator is x^4, and the highest power of x in the denominator is x^3. To simplify the limit, we can divide both the numerator and the denominator by x^3, the highest power of x in the denominator.Simplify Numerator: Dividing each term in the numerator by x^3 gives us: (-5x^4)/x^3 + (2x)/x^3 This simplifies to: -5x + 2/x^2Take Limits: Now, we take the limit of each term as x approaches infinity: lim_(x -> oo)(-5x) = -5 * lim_(x -> oo)(x) = -5 * infinity = -infinity lim_(x -> oo)(2/x^2) = 2 * lim_(x -> oo)(1/x^2) = 2 * 0 = 0Add Limits: Adding the limits of the individual terms, we get: lim_(x -> oo)(-5x + 2/x^2) = -infinity + 0 = -infinityFinal Answer: Since the limit of the function as x approaches infinity is -infinity, the limit is unbounded. Therefore, the correct answer is: (D) The limit is unbounded

Find $\lim _{x \rightarrow \infty} \frac{-5 x^{4}+2 x}{x^{3}}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $2$ $\newline$ (B) $0$ $\newline$ (C) $-5$ $\newline$ (D) The limit is unbounded

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Find $\lim _{x \rightarrow \infty} \frac{-5 x^{4}+2 x}{x^{3}}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $2$ $\newline$ (B) $0$ $\newline$ (C) $-5$ $\newline$ (D) The limit is unbounded