Question

evaluate the limit
lim_{x→∞} \frac{10x + 5}{2x^{2}-10x + 11}
question help: ▶ video

Explanation:

Step1: Divide by highest - power of x in denominator

Divide both the numerator and denominator by $x^{2}$. We get $\lim_{x
ightarrow\infty}\frac{\frac{10x}{x^{2}}+\frac{5}{x^{2}}}{\frac{2x^{2}}{x^{2}}-\frac{10x}{x^{2}}+\frac{11}{x^{2}}}=\lim_{x
ightarrow\infty}\frac{\frac{10}{x}+\frac{5}{x^{2}}}{2 - \frac{10}{x}+\frac{11}{x^{2}}}$.

Step2: Use limit rules

We know that $\lim_{x
ightarrow\infty}\frac{c}{x^{n}} = 0$ for any constant $c$ and positive integer $n$. So, $\lim_{x
ightarrow\infty}\frac{10}{x}=0$, $\lim_{x
ightarrow\infty}\frac{5}{x^{2}} = 0$, $\lim_{x
ightarrow\infty}\frac{10}{x}=0$ and $\lim_{x
ightarrow\infty}\frac{11}{x^{2}}=0$.

Step3: Evaluate the limit

Substitute the limit values into the expression: $\frac{0 + 0}{2-0 + 0}=0$.

Answer:

$0$