Question

homework 1.2: limits involving infinity
score: 0/36 answered: 0/18
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question 1
0/2 pts 8 49 details
evaluate the limit
lim_{x
ightarrow+infty}\frac{5 + 10x}{4 - 8x}
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Explanation:

Step1: Divide numerator and denominator by x

Divide both the numerator and denominator of $\frac{5 + 10x}{4-8x}$ by $x$. We get $\lim_{x
ightarrow\infty}\frac{\frac{5}{x}+ 10}{\frac{4}{x}-8}$.

Step2: Evaluate limits of individual terms

As $x
ightarrow\infty$, $\lim_{x
ightarrow\infty}\frac{5}{x}=0$ and $\lim_{x
ightarrow\infty}\frac{4}{x}=0$. So we have $\frac{0 + 10}{0-8}$.

Step3: Simplify the fraction

$\frac{10}{-8}=-\frac{5}{4}$.

Answer:

$-\frac{5}{4}$