Let f(x)=(-6x^(2)+x-1)/(x^(2)+3). Find lim_(x rarr oo)f(x). Choose 1 answer: (A) -(1)/(3) (B) -6 (C) 0 (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 as x grows without bound.Degree of polynomials in numerator and denominator: The degree of the polynomial in the numerator is 2 (because of the term -6x^2), and the degree of the polynomial in the denominator is also 2 (because of the term x^2).Limit as x approaches infinity: 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 -6, and the leading coefficient of the denominator is 1.Simplification of the limit: Therefore, the limit of f(x) as x approaches infinity is -6/1, which simplifies to -6.

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

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

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Full solution

Q. Let

f(x)=\frac{-6 x^{2}+x-1}{x^{2}+3}

\newline

Find

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

\newline

Choose

1

answer:

\newline

(A)

-\frac{1}{3}

\newline

(B)

-6

\newline

(C)

0

\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 as $x$ grows without bound.
Degree of polynomials in numerator and denominator: The degree of the polynomial in the numerator is $2$ (because of the term $-6x^2$ ), and the degree of the polynomial in the denominator is also $2$ (because of the term $x^2$ ).
Limit as $x$ approaches infinity: 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 $-6$ , and the leading coefficient of the denominator is $1$ .
Simplification of the limit: Therefore, the limit of $f(x)$ as $x$ approaches infinity is $-\frac{6}{1}$ , which simplifies to $-6$ .