lim_(x rarr oo)(-4x^(2)+3x+6)/(2x^(2)+1x-8)=_____

Analyze Behavior of Terms: To find the limit of the function as x approaches infinity, we need to analyze the behavior of the numerator and the denominator. Since both the numerator and the denominator are polynomials of the same degree (degree 2), we can compare the leading coefficients of the x^2 terms.Compare Leading Coefficients: The leading term in the numerator is -4x^2 and the leading term in the denominator is 2x^2. To find the limit as x approaches infinity, we can divide the coefficients of the leading terms.Divide Coefficients: Dividing the coefficients of the leading terms gives us -4/2, which simplifies to -2.Find Limit: Therefore, the limit of the function as x approaches infinity is -2.

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lim_(x rarr oo)(-4x^(2)+3x+6)/(2x^(2)+1x-8)=_____

$\lim _{x \rightarrow \infty} \frac{-4 x^{2}+3 x+6}{2 x^{2}+1 x-8}=\_\_\_\_\_$

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Algebra 2

Sum of finite series starts from 1

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\lim _{x \rightarrow \infty} \frac{-4 x^{2}+3 x+6}{2 x^{2}+1 x-8}=\_\_\_\_\_

Analyze Behavior of Terms: To find the limit of the function as $x$ approaches infinity, we need to analyze the behavior of the numerator and the denominator. Since both the numerator and the denominator are polynomials of the same degree (degree $2$ ), we can compare the leading coefficients of the $x^2$ terms.
Compare Leading Coefficients: The leading term in the numerator is $-4x^2$ and the leading term in the denominator is $2x^2$ . To find the limit as $x$ approaches infinity, we can divide the coefficients of the leading terms.
Divide Coefficients: Dividing the coefficients of the leading terms gives us $-4/2$ , which simplifies to $-2$ .
Find Limit: Therefore, the limit of the function as $x$ approaches $\infty$ is $-2$ .