Evaluate the following limit: _ x (3x-1)(4x-2) (x+8)(x-1) - Vidyadip

Question

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow{\infty}}\frac{(3\text{x}-1)(4\text{x}-2)}{(\text{x}+8)(\text{x}-1)}$

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Answer

$\lim\limits_{\text{x}\rightarrow{\infty}}\frac{(3\text{x}-1)(4\text{x}-2)}{(\text{x}+8)(\text{x}-1)}$ $\Big[\text{Expression is }\frac\infty\infty\Big]$ $=\lim\limits_{\text{x}\rightarrow{\infty}}\frac{\big(12\text{x}^2-10\text{x}+2\big)}{\big(\text{x}^2+9\text{x}-8\big)}$ $=\lim\limits_{\text{x}\rightarrow{\infty}}\Bigg(\frac{12-\frac{10}{\text{x}}+\frac{2}{\text{x}^2}}{1+\frac{9}{\text{x}}-\frac{8}{\text{x}^2}}\Bigg)$ $=\frac{12-0+0}{1+0-1}$ $=12$

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