Find lim_(x rarr oo)(-4x^(3)+5x)/(2x^(3)+7). Choose 1 answer: (A) (5)/(7) (B) -2 (C) 0 (D) The limit is unbounded

Divide by x^3: To find the limit of the given function as x approaches infinity, we can divide the numerator and the denominator by the highest power of x present in the function, which is x^3 in this case.Simplify terms: Divide each term in the numerator and the denominator by x^3: lim_(x rarr oo)((-4x^(3)/x^(3))+(5x/x^(3)))/((2x^(3)/x^(3))+(7/x^(3))). Simplify each term: lim_(x rarr oo)((-4)+(5/x^2))/((2)+(7/x^3)).Approach infinity: As x approaches infinity, the terms with x in the denominator (5/x^2 and 7/x^3) approach 0: lim_(x rarr oo)((-4)+0)/((2)+0). This simplifies to: lim_(x rarr oo)(-4)/(2).Calculate limit: Calculate the simplified limit: lim_(x rarr oo)(-4)/(2) = -2.

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Find derivatives of logarithmic functions

Full solution

Q. Find

\lim _{x \rightarrow \infty} \frac{-4 x^{3}+5 x}{2 x^{3}+7}

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Choose

1

answer:

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(A)

\frac{5}{7}

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(B)

-2

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(C)

0

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(D) The limit is unbounded

Divide by $x^3$ : To find the limit of the given function as $x$ approaches infinity, we can divide the numerator and the denominator by the highest power of $x$ present in the function, which is $x^3$ in this case.
Simplify terms: Divide each term in the numerator and the denominator by $x^3$ : $\lim_{x \to \infty}\left(\frac{-4x^{3}}{x^{3}}+\frac{5x}{x^{3}}\right)/\left(\frac{2x^{3}}{x^{3}}+\frac{7}{x^{3}}\right)$ . Simplify each term: $\lim_{x \to \infty}\left(\frac{-4+\frac{5}{x^2}}{2+\frac{7}{x^3}}\right)$ .
Approach infinity: As $x$ approaches infinity, the terms with $x$ in the denominator ( $\frac{5}{x^2}$ and $\frac{7}{x^3}$ ) approach $0$ : $\lim_{x \to \infty}\left(\frac{-4+0}{2+0}\right)$ .This simplifies to: $\lim_{x \to \infty}\left(\frac{-4}{2}\right)$ .
Calculate limit: Calculate the simplified limit: \lim_{x \rightarrow \infty}\frac{$-4$}{$2$} = \(-2\.