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

Step 1: Divide by highest power of x: 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.Step 2: Simplify by canceling out x^3 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))).Step 3: Evaluate terms with x in the denominator: Simplify the expression by canceling out the x^3 terms: lim_(x rarr oo)((-4)+(5/x^2))/((2)+(7/x^3)).Step 4: Simplify the expression: 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).Step 5: Calculate the limit: The expression simplifies to: lim_(x rarr oo)(-4)/(2).Calculate the simplified limit: lim_(x rarr oo)(-4)/(2) = -2.

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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

Find $\lim _{x \rightarrow \infty} \frac{-4 x^{3}+5 x}{2 x^{3}+7}$ . $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{5}{7}$ $\newline$ (B) $-2$ $\newline$ (C) $0$ $\newline$ (D) The limit is unbounded

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Algebra 2

Add, subtract, multiply, and divide polynomials

Full solution

Q. Find

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

\newline

Choose

1

answer:

\newline

(A)

\frac{5}{7}

\newline

(B)

-2

\newline

(C)

0

\newline

(D) The limit is unbounded

Step $1$ : Divide by highest power of $x$ : 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.
Step $2$ : Simplify by canceling out $x^3$ terms: Divide each term in the numerator and the denominator by $x^3$ : $\lim_{x \rightarrow \infty}\left(\frac{-4x^{3}/x^{3}}{2x^{3}/x^{3}}+\frac{5x/x^{3}}{7/x^{3}}\right)$ .
Step $3$ : Evaluate terms with x in the denominator: Simplify the expression by canceling out the $x^3$ terms: $\newline$ $\lim_{x \rightarrow \infty}\left(\frac{-4+\frac{5}{x^2}}{2+\frac{7}{x^3}}\right).$
Step $4$ : Simplify the expression: As $x$ approaches infinity, the terms with $x$ in the denominator ( $\frac{5}{x^2}$ and $\frac{7}{x^3}$ ) approach $0$ : $\lim_{x \rightarrow \infty}\frac{(-4)+0}{(2)+0}.$
Step $5$ : Calculate the limit: The expression simplifies to: $\lim_{x \rightarrow \infty}\left(\frac{-4}{2}\right)$ .
Step $5$ : Calculate the limit: The expression simplifies to: $\lim_{x \rightarrow \infty}\left(\frac{-4}{2}\right)$ .Calculate the simplified limit: $\lim_{x \rightarrow \infty}\left(\frac{-4}{2}\right) = -2$ .