Question

hw6 limits at infinity and asymptotes (target l3; 52.2,4.6)
score: 2/6 answered: 2/6
question 3
evaluate the limit
lim_{x
ightarrowinfty}\frac{7x^{2}-10x + 6}{8x+1}
question help: video message instructor

Explanation:

Step1: Divide by highest - power of x

Divide both the numerator and denominator by $x$ (since the highest - power of $x$ in the denominator is $x^1$). We have $\lim_{x
ightarrow\infty}\frac{7x^{2}-10x + 6}{8x+1}=\lim_{x
ightarrow\infty}\frac{\frac{7x^{2}}{x}-\frac{10x}{x}+\frac{6}{x}}{\frac{8x}{x}+\frac{1}{x}}=\lim_{x
ightarrow\infty}\frac{7x - 10+\frac{6}{x}}{8+\frac{1}{x}}$.

Step2: Analyze the limits of each term

As $x
ightarrow\infty$, $\lim_{x
ightarrow\infty}\frac{6}{x}=0$ and $\lim_{x
ightarrow\infty}\frac{1}{x}=0$. Also, $\lim_{x
ightarrow\infty}(7x - 10)=\infty$ and $\lim_{x
ightarrow\infty}(8)=8$. So, $\lim_{x
ightarrow\infty}\frac{7x - 10+\frac{6}{x}}{8+\frac{1}{x}}=\infty$.

Answer:

$\infty$