Question

question determine the limit shown below in simplest form. (limlimits_{x \to 0} \frac{x^2 + 3x}{x^2 + 7x})

Explanation:

Step1: Factor numerator and denominator

Factor \(x\) from numerator and denominator: \(\frac{x(x + 3)}{x(x + 7)}\) (note \(x
eq0\) as we take limit as \(x\to0\), so we can cancel \(x\))

Step2: Cancel common factor \(x\)

After canceling \(x\), we get \(\frac{x + 3}{x + 7}\)

Step3: Substitute \(x = 0\)

Substitute \(x = 0\) into \(\frac{x + 3}{x + 7}\): \(\frac{0 + 3}{0 + 7}=\frac{3}{7}\)

Answer:

\(\frac{3}{7}\)