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Let
f(x)=(6x^(3))/(3x+2).
Find
lim_(x rarr oo)f(x).
Choose 1 answer:
(A) 2
(B) 3
(c) 0
(D) The limit is unbounded

Let $f(x)=\frac{6 x^{3}}{3 x+2}$ . $\newline$ Find $\lim _{x \rightarrow \infty} f(x)$ . $\newline$ Choose $1$ answer: $\newline$ (A) $2$ $\newline$ (B) $3$ $\newline$ (C) $0$ $\newline$ D The limit is unbounded

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Is (x, y) a solution to the system of equations?

Full solution

Q. Let

f(x)=\frac{6 x^{3}}{3 x+2}

.

\newline

Find

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

.

\newline

Choose

1

answer:

\newline

(A)

2

\newline

(B)

3

\newline

(C)

0

\newline

D The limit is unbounded

Analyze degrees of polynomials: To find the limit of the function $f(x)$ as $x$ approaches infinity, we can analyze the degrees of the polynomials in the numerator and the denominator. $f(x) = \frac{6x^3}{3x + 2}$ The degree of the polynomial in the numerator is $3$ (since the highest power of $x$ is $x^3$ ), and the degree of the polynomial in the denominator is $1$ (since the highest power of $x$ is $x$ ).
Comparison of degrees: When the degree of the polynomial in the numerator is higher than the degree of the polynomial in the denominator, as $x$ approaches infinity, the function will also approach infinity. $\newline$ This is because the $x^3$ term in the numerator will grow much faster than the $3x$ term in the denominator as $x$ becomes very large.
Limit as $x$ approaches infinity: Therefore, the limit of $f(x)$ as $x$ approaches infinity is unbounded. $\newline$ $\lim_{x \to \infty} f(x) = \infty$

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