Let g(x)=(5x)/(5x^(4)-4). Find lim_(x rarr oo)g(x). Choose 1 answer: (A) -(5)/(4) (B) 1 (c) 0 (D) The limit is unbounded

Divide by x^4: We have g(x) = (5x) / (5x^4 - 4). To find the limit as x approaches infinity, we can divide every term in the numerator and the denominator by x^4, the highest power of x in the denominator.Simplify the expression: Dividing each term by x^4 gives us: g(x) = (5x/x^4) / (5x^4/x^4 - 4/x^4) Simplifying this, we get: g(x) = (5/x^3) / (5 - 4/x^4)Apply limit as x approaches infinity: As x approaches infinity, the terms with x in the denominator approach zero. Therefore, 5/x^3 approaches 0 and 4/x^4 also approaches 0.Calculate the final limit: Taking the limit as x approaches infinity, we get: lim_(x -> oo) g(x) = (0) / (5 - 0) This simplifies to: lim_(x -> oo) g(x) = 0 / 5Conclusion: Finally, we find that the limit of g(x) as x approaches infinity is 0. lim_(x -> oo) g(x) = 0

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Math Problems

Algebra 2

Add, subtract, multiply, and divide polynomials

Full solution

Q. Let

g(x)=\frac{5 x}{5 x^{4}-4}

\newline

Find

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

\newline

Choose

1

answer:

\newline

(A)

-\frac{5}{4}

\newline

(B)

1

\newline

(C)

0

\newline

D The limit is unbounded

Divide by $x^4$ : We have $g(x) = \frac{5x}{5x^4 - 4}$ . To find the limit as $x$ approaches infinity, we can divide every term in the numerator and the denominator by $x^4$ , the highest power of $x$ in the denominator.
Simplify the expression: Dividing each term by $x^4$ gives us: $\newline$ g(x) = $\frac{5x/x^4}{5x^4/x^4 - 4/x^4}$ $\newline$ Simplifying this, we get: $\newline$ g(x) = $\frac{5/x^3}{5 - 4/x^4}$
Apply limit as $x$ approaches infinity: As $x$ approaches infinity, the terms with $x$ in the denominator approach zero. Therefore, $\frac{5}{x^3}$ approaches $0$ and $\frac{4}{x^4}$ also approaches $0$ .
Calculate the final limit: Taking the limit as $x$ approaches infinity, we get: $\newline$ $\lim_{x \to \infty} g(x) = \frac{0}{5 - 0}$ $\newline$ This simplifies to: $\newline$ $\lim_{x \to \infty} g(x) = \frac{0}{5}$
Conclusion: Finally, we find that the limit of $g(x)$ as $x$ approaches infinity is $0$ . $\lim_{x \to \infty} g(x) = 0$