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

Analyze behavior of numerator and denominator: To find the limit of the function f(x) as x approaches infinity, we need to analyze the behavior of the numerator and the denominator separately. We will look for the highest power of x in both the numerator and the denominator to simplify the expression.Divide by highest power of x: The highest power of x in the numerator is x^2, and in the denominator, it is x^3. To simplify the limit, we can divide both the numerator and the denominator by x^3, which is the highest power of x in the denominator.Simplify the expression: Dividing each term in the numerator and the denominator by x^3 gives us: f(x) = [(-2x^2/x^3) + (5x/x^3)] / [(4x^3/x^3) - (2x/x^3) + (1/x^3)] Simplifying each term, we get: f(x) = [(-2/x) + (5/x^2)] / [4 - (2/x^2) + (1/x^3)]Terms with x in denominator approach zero: As x approaches infinity, the terms with x in the denominator will approach zero. Therefore, (-2/x), (5/x^2), (2/x^2), and (1/x^3) will all approach zero.Evaluate the limit: After the terms with x in the denominator approach zero, we are left with: lim_(x -> oo)f(x) = 0 / 4Final result: Simplifying the expression, we get: lim_(x -> oo)f(x) = 0

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

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

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Full solution

Q. Let

f(x)=\frac{-2 x^{2}+5 x}{4 x^{3}-2 x+1}

\newline

Find

\lim _{x \rightarrow \infty} f(x)

\newline

Choose

1

answer:

\newline

(A)

0

\newline

(B)

5

\newline

(C)

-\frac{1}{2}

\newline

(D) The limit is unbounded

Analyze behavior of numerator and denominator: To find the limit of the function $f(x)$ as $x$ approaches infinity, we need to analyze the behavior of the numerator and the denominator separately. We will look for the highest power of $x$ in both the numerator and the denominator to simplify the expression.
Divide by highest power of x: The highest power of $x$ in the numerator is $x^2$ , and in the denominator, it is $x^3$ . To simplify the limit, we can divide both the numerator and the denominator by $x^3$ , which is the highest power of $x$ in the denominator.
Simplify the expression: Dividing each term in the numerator and the denominator by $x^3$ gives us: $\newline$ f(x) = $[(-2x^2/x^3) + (5x/x^3)] / [(4x^3/x^3) - (2x/x^3) + (1/x^3)]$ $\newline$ Simplifying each term, we get: $\newline$ f(x) = $[(-2/x) + (5/x^2)] / [4 - (2/x^2) + (1/x^3)]$
Terms with $x$ in denominator approach zero: As $x$ approaches infinity, the terms with $x$ in the denominator will approach zero. Therefore, $(-\frac{2}{x})$ , $(\frac{5}{x^2})$ , $(\frac{2}{x^2})$ , and $(\frac{1}{x^3})$ will all approach zero.
Evaluate the limit: After the terms with $x$ in the denominator approach zero, we are left with: $\lim_{x \to \infty}f(x) = \frac{0}{4}$
Final result: Simplifying the expression, we get: $\lim_{x \to \infty}f(x) = 0$