lim_(x rarr oo)(75 x+25)/(x^(3)+x+2)=_____

Divide by x^3: To find the limit of the function as x approaches infinity, we need to analyze the behavior of the numerator and the denominator separately. The highest power of x in the denominator is x^3, so we should divide every term in the numerator and the denominator by x^3 to simplify the expression.Simplify the function: After dividing each term by x^3, the function becomes: lim_(x rarr oo) (75/x^2 + 25/x^3) / (1 + 1/x^2 + 2/x^3)Terms approach 0: As x approaches infinity, the terms with x in the denominator approach 0. Therefore, the function simplifies to: lim_(x rarr oo) (0 + 0) / (1 + 0 + 0)Calculate the limit: The limit of the function as x approaches infinity is then: 0 / 1 = 0

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lim_(x rarr oo)(75 x+25)/(x^(3)+x+2)=_____

$\lim _{x \rightarrow \infty} \frac{75 x+25}{x^{3}+x+2}=\_\_\_\_\_$

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Algebra 2

Sum of finite series starts from 1

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\lim _{x \rightarrow \infty} \frac{75 x+25}{x^{3}+x+2}=\_\_\_\_\_

Divide by $x^3$ : To find the limit of the function as $x$ approaches infinity, we need to analyze the behavior of the numerator and the denominator separately. The highest power of $x$ in the denominator is $x^3$ , so we should divide every term in the numerator and the denominator by $x^3$ to simplify the expression.
Simplify the function: After dividing each term by $x^3$ , the function becomes: $\lim_{x \rightarrow \infty} \frac{75/x^2 + 25/x^3}{1 + 1/x^2 + 2/x^3}$
Terms approach $0$ : As $x$ approaches infinity, the terms with $x$ in the denominator approach $0$ . Therefore, the function simplifies to: $\lim_{x \rightarrow \infty} \frac{(0 + 0)}{(1 + 0 + 0)}$
Calculate the limit: The limit of the function as $x$ approaches infinity is then: $\frac{0}{1} = 0$