Question

18 numeric 2 points use the algebraic method to compute $lim_{x \to 0} \frac{x}{x^{2}+5x}$. note: for this auto - graded quiz, you need only give the final numerical answer. but notation correctly in your work! give your answer as a decimal number, rounded to one decimal place. answer

Explanation:

Step1: Factor the denominator

Factor $x^{2}+5x$ as $x(x + 5)$. So the limit becomes $\lim_{x
ightarrow0}\frac{x}{x(x + 5)}$.

Step2: Simplify the expression

Cancel out the common - factor $x$ (since $x
eq0$ when taking the limit). We get $\lim_{x
ightarrow0}\frac{1}{x + 5}$.

Step3: Substitute the value of $x$

Substitute $x = 0$ into $\frac{1}{x+5}$. We have $\frac{1}{0 + 5}=\frac{1}{5}=0.2$.

Answer:

$0.2$