evaluate the limit\n lim _ { x \rightarrow infty } \frac { 7 x ^ { 3 } - 9 x ^ { 2 } - 7 x } { 10 - 6 x - 8…

evaluate the limit\n lim _ { x \rightarrow infty } \frac { 7 x ^ { 3 } - 9 x ^ { 2 } - 7 x } { 10 - 6 x - 8 x ^ { 3 } }

evaluate the limit\n lim _ { x \rightarrow infty } \frac { 7 x ^ { 3 } - 9 x ^ { 2 } - 7 x } { 10 - 6 x - 8 x ^ { 3 } }

Answer

Explanation:

Step1: Divide numerator and denominator by (x^3)

$$\lim_{x\rightarrow\infty}\frac{7x^{3}-9x^{2}-7x}{10 - 6x-8x^{3}}=\lim_{x\rightarrow\infty}\frac{\frac{7x^{3}}{x^{3}}-\frac{9x^{2}}{x^{3}}-\frac{7x}{x^{3}}}{\frac{10}{x^{3}}-\frac{6x}{x^{3}}-\frac{8x^{3}}{x^{3}}}$$

Step2: Simplify each term

$$=\lim_{x\rightarrow\infty}\frac{7-\frac{9}{x}-\frac{7}{x^{2}}}{\frac{10}{x^{3}}-\frac{6}{x^{2}}-8}$$

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

As (x\rightarrow\infty), (\frac{9}{x}\rightarrow0), (\frac{7}{x^{2}}\rightarrow0), (\frac{10}{x^{3}}\rightarrow0), (\frac{6}{x^{2}}\rightarrow0) $$=\frac{7 - 0-0}{0 - 0-8}$$

Answer:

(-\frac{7}{8})