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

Question

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

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Divide by highest power of x: To find the limit of the given function as x approaches infinity, we can divide the numerator and the denominator by the highest power of x present in the function, which is $ x^4 $. $$ \lim_{x \to \infty} \frac{5x^4 + x^2}{2x^4 - x^3 - 4} = \lim_{x \to \infty} \frac{\frac{5x^4}{x^4} + \frac{x^2}{x^4}}{\frac{2x^4}{x^4} - \frac{x^3}{x^4} - \frac{4}{x^4}} $$Simplify expression: Now we simplify the expression by canceling out the $ x^4 $ terms and reducing the other terms by their respective powers of x. $$ \lim_{x \to \infty} \frac{5 + \frac{1}{x^2}}{2 - \frac{1}{x} - \frac{4}{x^4}} $$Remove terms with x in denominator: As x approaches infinity, the terms with $ x $ in the denominator will approach zero. Therefore, we can simplify the expression further by removing those terms. $$ \lim_{x \to \infty} \frac{5 + 0}{2 - 0 - 0} = \frac{5}{2} $$Evaluate the limit: The limit of the function as x approaches infinity is $ \frac{5}{2} $. This corresponds to answer choice (A).

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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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