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

Degree Comparison: To find the limit of the given function as x approaches infinity, we can compare the degrees of the polynomials in the numerator and the denominator.Leading Coefficients: The degree of the polynomial in the numerator is 3 (because of the term 3x^3), and the degree of the polynomial in the denominator is also 3 (because of the term x^3).Limit Calculation: When the degrees of the polynomials in the numerator and the denominator are the same, the limit as x approaches infinity is the ratio of the leading coefficients.The leading coefficient of the numerator is 3 (from the term 3x^3), and the leading coefficient of the denominator is 1 (from the term x^3).Therefore, the limit as x approaches infinity of (3x^3 - 5x) / (x^3 - 2x^2 + 1) is 3/1, which simplifies to 3.

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

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

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Algebra 2

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Full solution

Q. Find

\lim _{x \rightarrow \infty} \frac{3 x^{3}-5 x}{x^{3}-2 x^{2}+1}

\newline

Choose

1

answer:

\newline

(A)

-5

\newline

(B)

0

\newline

(C)

3

\newline

(D) The limit is unbounded

Degree Comparison: To find the limit of the given function as $x$ approaches $\infty$ , we can compare the degrees of the polynomials in the numerator and the denominator.
Leading Coefficients: The degree of the polynomial in the numerator is $3$ (because of the term $3x^3$ ), and the degree of the polynomial in the denominator is also $3$ (because of the term $x^3$ ).
Limit Calculation: When the degrees of the polynomials in the numerator and the denominator are the same, the limit as $x$ approaches $\infty$ is the ratio of the leading coefficients.
Limit Calculation: When the degrees of the polynomials in the numerator and the denominator are the same, the limit as $x$ approaches infinity is the ratio of the leading coefficients.The leading coefficient of the numerator is $3$ (from the term $3x^3$ ), and the leading coefficient of the denominator is $1$ (from the term $x^3$ ).
Limit Calculation: When the degrees of the polynomials in the numerator and the denominator are the same, the limit as $x$ approaches infinity is the ratio of the leading coefficients.The leading coefficient of the numerator is $3$ (from the term $3x^3$ ), and the leading coefficient of the denominator is $1$ (from the term $x^3$ ).Therefore, the limit as $x$ approaches infinity of $(3x^3 - 5x) / (x^3 - 2x^2 + 1)$ is $3/1$ , which simplifies to $3$ .