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

Divide by x^4: To find the limit of the given function as x approaches infinity, we can divide each term in the numerator and the denominator by the highest power of x present in the denominator, which is x^4.Simplify numerator: Divide each term in the numerator by x^4: (5x^4/x^4) + (x^2/x^4) = 5 + (1/x^2)Simplify denominator: Divide each term in the denominator by x^4: (2x^4/x^4) - (x^3/x^4) - (4/x^4) = 2 - (1/x) - (4/x^4)Rewrite limit expression: Now, we rewrite the original limit expression with the simplified terms: lim_(x rarr oo) (5 + (1/x^2)) / (2 - (1/x) - (4/x^4))Approach infinity: As x approaches infinity, the terms with x in the denominator approach zero. Therefore, (1/x^2), (1/x), and (4/x^4) all approach zero.Simplify further: The limit expression simplifies to: lim_(x rarr oo) (5 + 0) / (2 - 0 - 0) = 5/2Final result: The limit of the function as x approaches infinity is 5/2, which corresponds to answer choice (A).

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

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

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Q. Find

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

\newline

Choose

1

answer:

\newline

(A)

\frac{5}{2}

\newline

(B)

0

\newline

(C)

-\frac{1}{4}

\newline

(D) The limit is unbounded

Divide by $x^4$ : To find the limit of the given function as $x$ approaches infinity, we can divide each term in the numerator and the denominator by the highest power of $x$ present in the denominator, which is $x^4$ .
Simplify numerator: Divide each term in the numerator by $x^4$ : $(5x^4/x^4) + (x^2/x^4) = 5 + (1/x^2)$
Simplify denominator: Divide each term in the denominator by $x^4$ : $(\frac{2x^4}{x^4}) - (\frac{x^3}{x^4}) - (\frac{4}{x^4}) = 2 - (\frac{1}{x}) - (\frac{4}{x^4})$
Rewrite limit expression: Now, we rewrite the original limit expression with the simplified terms: $\lim_{x \rightarrow \infty} \frac{5 + \frac{1}{x^2}}{2 - \frac{1}{x} - \frac{4}{x^4}}$
Approach infinity: As $x$ approaches infinity, the terms with $x$ in the denominator approach zero. Therefore, $\frac{1}{x^2}$ , $\frac{1}{x}$ , and $\frac{4}{x^4}$ all approach zero.
Simplify further: The limit expression simplifies to: $\lim_{x \rightarrow \infty} (5 + 0) / (2 - 0 - 0) = \frac{5}{2}$
Final result: The limit of the function as $x$ approaches infinity is $\frac{5}{2}$ , which corresponds to answer choice (A).