find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriate. if the limit does not otherwise…

find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriate. if the limit does not otherwise exist, enter dne.)\n\\( \\lim _ { x \\rightarrow \\infty } \\frac { 9 x - 2 } { 2 x + 3 } \\)

find the limit. (if the limit is infinite, enter ∞ or -∞, as appropriate. if the limit does not otherwise exist, enter dne.)\n\\( \\lim _ { x \\rightarrow \\infty } \\frac { 9 x - 2 } { 2 x + 3 } \\)

Answer

Explanation:

Step1: Divide numerator and denominator by (x)

$$\lim_{x\rightarrow\infty}\frac{9x - 2}{2x + 3}=\lim_{x\rightarrow\infty}\frac{\frac{9x}{x}-\frac{2}{x}}{\frac{2x}{x}+\frac{3}{x}}$$

Step2: Simplify the expression

$$=\lim_{x\rightarrow\infty}\frac{9-\frac{2}{x}}{2+\frac{3}{x}}$$

Step3: Use the limit property (\lim_{x\rightarrow\infty}\frac{c}{x}=0) ((c) is a constant)

As (x\rightarrow\infty), (\lim_{x\rightarrow\infty}\frac{2}{x}=0) and (\lim_{x\rightarrow\infty}\frac{3}{x}=0). So the limit becomes (\frac{9 - 0}{2+0})

Answer:

(\frac{9}{2})